In the abstract: According to Rambam, the laws of impurity are not related to intrinsic spiritual status. They are rather legal categories that relate to historic social psychological perceptions.
Rambam has a chapter in Moreh Nevukhim (3:47) devoted to ritual impurity. It seems worthwhile to see the entire chapter. The following is an elided translation of the text, with the portions most relevant to the question emphasised:
I maintain that the Law which was revealed to Moses, our Teacher, and which is called by his name, aims at facilitating the service and lessening the burden, and if a person complains that certain precepts cause him pain and great trouble, he cannot have thought of the habits and doctrines that were general in those days...
This is the great principle which you must never lose sight of. After having stated this principle, I repeat that the whole intention with regard to the sanctuary was to create in the hearts of those who enter it certain feelings of awe and reverence, in accordance with the command, "You shall reverence my sanctuary" (Lev. xix. 30). But when we continually see an object, however sublime it may be, our regard for that object will be lessened, and the impression we have received of it will be weakened...
For this reason the unclean were not allowed to enter the Sanctuary, although there are so many kinds of uncleanliness, that [at a time] only a few people are clean. For even if a person does not touch a beast that died of its own accord (Lev. xi. 27), he can scarcely avoid touching one of the eight kinds of creeping animals (ibid. 29, seq.), the dead bodies of which we find at all times in houses, in food and drink, and upon which we frequently tread wherever we walk; and, if he avoids touching these, he may touch a woman in her separation (ibid. xv. 18), or a male or female that have a running issue (ibid. ver. 1, seq. and 25, seq.), or a leper (ibid. xiii. 46), or their bed (ibid. xv. 5). Escaping these, he may become unclean by cohabitation with his wife, or by pollution (ibid. 15), and even when he has cleansed himself from any of these kinds of uncleanliness, he cannot enter the Sanctuary till after sunset; but not being enabled to enter the Sanctuary at night time, although he is clean after sunset, as may be inferred from Middot and Tamid, he is again, during the night, subject to becoming unclean either by cohabiting with his wife or by some other source of uncleanliness, and may rise in the morning in the same condition as the day before. All this serves to keep people away from the Sanctuary, and to prevent them from entering it whenever they liked...
The easier the diffusion of uncleanliness is, the more difficult and the more retarded is its purification...The uncleanness caused by a woman having running issue or during her separation is more frequent than that caused by contact with unclean objects: seven days are therefore required for their purification (Lev. xv. 19, 28), whilst those that touch them are only unclean one day
All these cases of uncleanliness, viz., running issue of males or females, menstruations, leprosy, dead bodies of human beings, carcasses of beasts and creeping things, and issue of semen, are disgusting. We have thus shown that the above precepts are very useful in many respects. First, they keep us at a distance from disgusting things; secondly, they guard the Sanctuary; thirdly, they pay regard to an established custom (for the Sabeans submitted to very troublesome restrictions when unclean, as you will soon hear); fourthly, they lightened that burden for us; for we are not impeded through these laws in our ordinary occupations by the distinction the Law makes between that which is unclean and that which is clean. For this distinction applies only in reference to the Sanctuary and the holy objects connected with it: it does not apply to other cases...
Other persons [that do not intend to enter the Sanctuary or touch any holy thing], are not guilty of any sin if they remain unclean as long as they like, and eat, according to their pleasure, ordinary food that has been in contact with unclean things. But the practice of the Sabeans... was to keep a menstruous woman in a house by herself, to burn that upon which she treads, and to consider as unclean every one that speaks with her: even if a wind passed over her and a clean person, the latter was unclean in the eyes of the Sabeans. See the difference between this practice and our rule, that "whatever services a wife generally does to her husband, she may do to him in her separation"; only cohabitation is prohibited during the days of her uncleanness.
Another custom among the Sabeans, which is still widespread, is this: whatever is separated from the body, as hair, nail, or blood, is unclean... whenever a person passes a razor over his skin he must take a bath in running water. Such burdensome practices were numerous among the Sabeans, whilst we apply the laws that distinguish between the unclean and the clean only with regard to hallowed things and to the Sanctuary....
As it was very necessary that the high-priest should always be in the Sanctuary, in accordance with the Divine command, "And it shall always be on his forehead" (Exod. xxviii. 38), he was not permitted to defile himself by any dead body whatever, even of the above-named relatives (Lev. xxi. 10-12). Women were not engaged in sacrificial service; the above law consequently does not apply to women; it is addressed to "the sons of Aaron," and not to "the daughters of Aaron." (Friedlander translation with some corrections based on Pines).
In a similar vein, he writes in Hilkhot Tumat Okhlin (16:14) that the point of abstaining from impurity even when not mandated by the Law, is as a social technique to avoid the stratum of society that does not avoid it. Rather than seeing any spiritual benefit in purity (as does for example Ramban in his commentary to Leviticus (19:2)), he explains it purely socially:
אף על פי שמותר לאכול אוכלין טמאים ולשתות משקין טמאים, חסידים הראשונים היו אוכלין חוליהן בטהרה ונזהרין מן הטומאות כולן כל ימיהן; והן הנקראין פרושים. ודבר זה קדושה יתרה היא, ודרך חסידות שיהיה אדם נבדל ופורש משאר העם, ולא ייגע בהן ולא יאכל וישתה עימהן
Similarly, he writes in Hilkhot Issurei Biah (21:12) that the reason for the original enactment that a ba'al keri refrain from studying Torah, is in order to generally decrease sexual activity; not because there is something wrong with being impure:
ולא תיקנו בראשונה לבעלי קראין שלא יקראו בתורה עד שיטבולו, אלא כדי למעט בתשמיש המיטה.
(Which inevitably is tainted by my own understanding): The laws of impurity are structured to achieve desired ends. Rambam does not mention any intrinsic spiritual characteristic to ritual impurity. Rather, it seems that the primary focus of ritual impurity is as a means of limiting casual access to the Temple, and thereby concretising feeling of awe towards it. The length of time for various forms of impurity seems correlated not to the intrinsic characteristic of each form of impurity, but rather to the psychological effects thereof. The more common an encounter causes it, the less severe it is treated, and vice-versa. This fits with the idea that the point is to surround the Temple with an aura of awe. Things perceived as more normal and common pollutants require less pause, than those perceived as more abnormal.
This idea of impurity as a historic perceived characteristic (which in turn related to legal statuses) is part of Rambam's general scheme of viewing the mitsvot as relating particularly to the social and religious norms of the time. In our case, Rambam develops this into an additional reason for the laws of impurity; they relate to social and religious norms of the Sabean idolaters. In this case, they tended to be more stringent with many of these sources of impurity. The Torah's laws are meant then to provide an easier alternative to the Sabean system, meant specifically to engender respect for the Temple, and to avoid restrictive superstitions regarding menstruants, and other sources of impurity.
Fascinatingly, note Hilkhot Miqvaot (11:15) in which Rambam emphasises that the laws of impurity are not intuitive, and are certainly not meant to remove physical dirt:
דבר ברור וגלוי שהטומאות והטהרות גזירת הכתוב הן, ואינן מדברים שדעתו של אדם מכרעת אותן, והרי הן מכלל החוקים; וכן הטבילה מן הטומאות, מכלל החוקים היא: שאין הטומאה טיט או צואה שתעבור במים, אלא גזירת הכתוב היא
My impression (particularly in context of the above) is that he is emphasising that the laws of impurity are not the result of substances' characteristics. Rather, their classification is the result of their very externally imposed legal status!