Rav Moshe Feinstein zt'l says in many places that holiness is a pre-condition for being commanded in mitzvos (not the reverse). You'll note that a Cohen, who has more mitzvos, is more holy.
"The mitzvah of You shall be holy, which is followed by a recitation of several of the fundamental mitzvos, is not of the same type as the mitzvos that follow it. This mitzvah means that every Jew should realize that he is sanctified with the holiness of the Jew, and it is only because of that holiness that we were given the Torah and obligated to do the mitzvos. As I have often written, mitzvos cannot be fulfilled properly unless the doer has the holiness of the Jew. The Kohanim, who have additional mitzvos, must have the particular holiness of Kohanim. This is why we make a blessing before mitzvos and say, "Who has sanctified us with His mitzvos"; and Kohanim, before doing mitzvos that are limited to Kohanim, say, "Who has sanctified us with the sanctity of Aharon." The expression "Who has sanctified us with His mitzvos" should not be misunderstood as meaning that mitzvos are the source of the sanctity. It is self-understood that the sanctity the blessing refers to is the underlying sanctity of every Jew -- that which enables us to fulfill the mitzvos." Rav Moshe Feinstein, zt'l, Darash Moshe, Volume II, p. 154, Vayikra, Kedoshim
So what about the positive time bound mitzvos? Women have the holiness but are exempt in order to take care of the family. Every reference in the Torah to holiness mentions the men and women. They are in that sense equal in holiness. He implies here that the use of the word patur is because women have a connection to those mitzvos but are patur. To put it in my words, nobody says a man is patur from niddah. Nobody says a Yisroel is patur from birchos cohanim. You are only patur from a mitzvah that you might otherwise be commanded in. Reb Moshe:
"Regarding the distinguished (Jewish) ladies who are fighting along with women of the nations of the world in their (social) movement. These (Jewish) ladies are observant of Torah and want to bring their fight to matters of relevance to Jewish law. Some (of these ladies) pray with tallaisim and so on. They seek my view in this matter and how the rabbi of the shul should handle the matter.
Firstly, you must know that it is an essential matter of faith in our Torah that the written and oral Torah was given by The Holy One Himself at Mount Sinai through Moshe Rabbanu, o"h. It is impossible to change even one point (of the Torah) whether to be more strict or to be more lenient. But we were commanded that when there is a time to establish precautionary measures, it is incumbent on the Sanhedrin and the sages of the Torah to do so, by prohibiting certain things. They also may obligate others. They (the sages) must make it very clear that these are rabbinical obligations. Since our dispersion to foreign lands, we lack the power (to make such enactments). However, the wise men of every region (have the power) to make enactments only for their region and only for a short time.
In view of this, the exemption of women from positive time bound commandments is a (decree) of the Torah. Also, the Rabbis never obligated women (in these commandments) since there is no reason to do so. Indeed, there is a reason to exempt women from these commandments specifically for the reasons that the Torah exempts them.
And besides the reasons for the Torah which are unknown to regular people and to the great scholars, and we are required to believe that there are great reasons of Hashem who gave the Torah, (besides this), there are (non-ultimate) reasons revealed to everyone. (In the matter of the exemption of women from positive time bound mitzvahs) the average woman is not wealthy and has responsibility to raise sons and daughters. This (task) is most important work for Hashem and His Torah and so Hashem made each species so that the woman should raise the offspring. Humans are no exception. The nature of women enables them to raise children. Along those lines, it (the burden) was made easier on the women by not requiring them to learn Torah and to perform positive time bound mitzvahs.
(However) even if the order of the world were to change and all women were wealthy all the time and it were possible to give over the children to men and women (to raise them as is done) in our country, the Torah's law cannot change and neither can that of the Rabbis. It is useless to fight this. Even with the agreement of the entire world, there is no power to change (the Torah) one iota. The women who stubbornly wage war to make such changes are committing heresy.
The Rambam, in chapter three, law number eight, of the Laws on Repentance, says the following: "Three (people) are called heretics: The one who denies even one word spoken by Moshe Rabbainu, the one who denies the explanation of the oral Torah, and the one who switches one word (of Torah) for another. These are heretics and their judgment shall be a forfeiture of their place in the next world.” According to the words of the Rambam, to say that the Creator switches around commandments and all the more so that men can switch around the commandments -- is to say that the Torah is not eternal. And the whole reason (it is called heresy) is that they are rebelling against many verses which teach us of the eternity of the Torah, and so writes the Kesef Mishnah.
Women are permitted to perform (certain) commandments for which they are not obligated and receive divine reward for such performance. And also according to the view of Tosfos, (women) are permitted to make a blessing (on such commandments) as is our custom. (It is our custom also for women to be permitted) to fulfill the commandments of shofar and luluv and to make blessings (on these). Therefore, concerning tzittzit, a woman who wants can dress in a garment not designed for men, as long as this garment has four corners to it, and attach tzittzit to fulfill this commandment.
Concerning the wearing of tfellin, Tosfos writes in Eruvin 96, divray hamaskil: myachal, that (this commandment) should not be performed (by women). Tfellin requires tremendous care to keep the body in (halachic) cleanliness and to focus one's attention. For this reason even men who are obligated in tfellin limit their wearing (of tfellin) from all day to during morning prayers. The Rema holds similarly (Choshen Mishpat, 98:3). Targum Yonason, on the verse: "There should not be a man's clothing on a woman" (holds) that (women should not wear) tzitzit or tfellin since they are garments of men. Tosfos does not believe there to be such a Targum Yonason. This (performance of non-obligatory commandments by a woman) applies only if her soul yearns to perform the commandment even though she is not commanded. (It is another matter) if her intention is to protest against the Holy One and His Torah. Such a posture is not congruent with the performance of a commandment. Indeed, it is a forbidden act and an act of apostasy. Since (such a woman) is trying to amend Torah law.
You should know that all of this (the exemption of women from positive time bound commandments) is not because women are on a lower level of holiness than are men. While obligation in commandments results strictly from one's having holiness, men and women, in that sense, are equal in holiness. All the verses in the Torah regarding holiness refer also to women. (This applies from) the beginning (with) the arrangement to receive the Torah (at Sinai). "You'll be to me a treasure and you'll be to me a holy nation." Exodus 19:6. (The subject of this verse is all of the nation of Israel) as it says "house of Jacob" in referring to the women and "tell to the house of Israel" in referring to the men. Exodus 19:3.
(The references to men and women of all verses regarding holiness extends also after Sinai with) "You'll be for me a people of holiness," parshas Mishpatim, "you'll be holy," parshas Shimini, "holy you'll be and you'll be holy," parshas Kedoshim, and "and a nation of holy people you are to Hashem" parshas Re’eh. Women also (as well as men) are referred to in every mention of holiness.
Therefore women also include in their blessings the words "you have sanctified us with your commandments." (Women do this) even when performing commandments for which they are not obligated. (The exclusion of women from positive time bound commandments) is a leniency made by Hashem for his own reasons and not because of any diminution (regarding the women) Heaven forbid. We explained this earlier.
And concerning the obligations between husband and wife, a husband is obligated to treat his wife with respect and a wife is obligated to treat her husband with respect. (Furthermore) many women were prophetesses and subject to the same laws concerning prophets as were the men (prophets). In many matters, women were praised more than the men by the (written) Torah and by the Rabbis. There is no denigration in their (women's) respect in their exemption from the learning of Torah and positive time-bound commandments. There is no reason to have any gripes.
The distinguished rabbi (of the congregation in question) should explain this every time and be strong and firm in his knowledge that this is all a matter of the Torah and he should correct these women. And after all this if (these women) still stand in their incorrect and stubborn view, (the rabbi) should not allow a single change in the holy customs of Israel. I end with a blessing for true peace and a good writing and sealing for a good year for the distinguished rabbi and to all that is his, to the whole holy congregation, the men, the women, and the children."
Igros Moshe, Orach Chaim IV #49