We cannot reach cleanness from death unclenness nowadays, because of the lack of "Mey Chatas." We assume that everyone's "Tamei Meis." So, almost all hilchos Tumah v'Taharah are not practiced. Thus, why do we still hold of a part of rules of Tumah v'Taharah such as Netilas Yadayim, Niddah, and of a Kohen not becoming "Tamei Meis"?
This is a very good question. It is also broad. The question is that you assume that everybody is Tme Met. And without Me Hat'at, we remain Tme Met. Why, despite the situation of permanent Tum'a (i.e. until the next Para Aduma preparation), we need to continue to pay attention to Tum'a. .
Let's start with the most spread: Nidda (following the Sefer Hachinuch).
Nidda contains several rules; One of these concern sexual intercourse (Chinuch 207).
שלא לבוא על אשה בעת שהיא נדה, שנאמר (ויקרא יח יט) ואל אשה בנדת טמאתה לא תקרב.
Not to be in sexual relationship with a woman in time that she is nidda. ... And until the end of the 7 Yemei Nidda and Tvilat nidda, she is yet nidda (I skip here the problem of zava-nidda, but it must be known). A wife with Tum'at met is not prohibited for bia. Tum'at nida only is linked to the prohibition. The required
Tum'at Kohanim (2 views in Rishonim):
mitsvat 263, it is not related that the prohibition to be unclean with a dead is linked to the cleanness of the Kohen in the enunciation of the Mitsva.
In this Mishnayot it is ruled that if they prevent him, "don't be unclean, don't be unclean" and he makes himself unclean (again) despite the prevention, he will be flagellated for each of the warnings.
If he is already unclean, what is the "and he makes himself unclean again"?
The Tosfot Yom Tov on mishnayot Makkot summarize the Gemara; he makes himself unclean again when he moves of and touches again or lift (the dead) or covers it. He report also an other opinion following which the "making unclean again" must be new,e.g. covering after touching. He also makes a correlation between those opinions and a controversy between Rambam and Raavad in chapter 5 of Nezirut Halacha 15-17.
The origin of the Machloket is a Gemara in Nazir 42b.
Rambam learn that the conclusion of the Gemara is that someone that is tme met Shelobechiburim (i.e. that is no longer in contact with the death) and come back in contact with the dead reach an additional grade of tum'a. So, even for us, assuming that all people is tme met, to touch a dead or put in Ohel hamet is an additional tum'a. You can say it "don't be unclean" (i.e. e.g. don't touch the dead) and he will touch. He is Chayav Malkut.
For the Raavad, the conclusion of the Gemara is that Tum'at chiburim is not a law from Tora, and Kohen do not be flagelled for it. And there is no enhancement or cummulation of Tum'at met one after another.
If you want to understand this issue, read Teshuvat Harashba 324
This is a Gzera from Shlomo Hamelech mishum srach Truma. Milechatechilla it is not really for cleanness.
1.Nidda is not only a law of Tum'a but an Isur Bia at time of uncleanness of nidda, not uncleanness of death. (At time of Mikdash too, there are situations that Tum'at Met is allowed betsibur, but not Zav and Zava. Tum'ot are independent one to another.)
2.Netilat Yadaym is a Gzera derabanan in way not to forgot Tum'a of Truma.
3.The Tum'at Kohanim at time that we have no Me Hat'at. This is discussed on Rishonim and acharonim. For simplification. If a Kohen is surely Tme Met, p.e. he touched his dead father (allowed), May he enter in an Ohel Hamet? Machloket. Chibure Met, modern poskim ruled that it is prohibited. T
Blu Greenberg notes (I'll look into where a bit later) that the tumah of niddah is in some sense unrelated to the prohibition to a husband of relations with a niddah. The latter exists nowadays, but the former does not practically. For example, a chair or other furniture a niddah has sat on becomes ritually impure. Yet no one declines sitting where the niddah previously sat.
An analogy of sorts: An animal which died of non-shechita causes (a neveila) is ritually impure, and prohibited to eat. We don't practice the impurity, but we do practice the not eating it.
Kohanim are prohibited from becoming impure from a dead body (seemingly only directly, and not via other objects or people). [Leviticus 21:1] So even though they may well already be as impure as if they did touch a dead person, or attend a funeral, they are prohibited from again coming in contact, carrying, or being in a covering with a corpse.