Let me start by saying that I understand the general rules of niddah. However, I was initially very confused why the niddah period is still observed at all, even among Orthodox Jews, since the other forms of purity and impurity are no longer upheld. According to this article, Why Is Impurity Not Observed?, niddah seems to be the only purity rule that matters anymore to everyday folks.
I did find a reason why men cannot have sex with a woman in niddah.
Rabbi Avram Israel Reisner says in "Observing Niddah in Our Day: An Inquiry on the Status of Purity and the Prohibition of Sexual Activity with a Menstruant:"
With regard to sexual relations with a woman during her menses, the question to be investigated is, given that a menstruant cannot now defile non-existent sancta, is the ban on sexual relations with a menstruant still in force? Plainly, the answer to that question must be yes, for the Torah clearly prohibits cohabitation with a woman during her menses as a category of illicit sexual relations, without reference to matters of purity, in two separate verses, Vayikra 18.19 and 20.18.15
And this makes perfect sense. However, both of these verses refer just to sex.
Leviticus 18:19
Do not approach a woman to have sexual relations during the uncleanness of her monthly period.
Leviticus 20:18
If a man has sexual relations with a woman during her monthly period, he has exposed the source of her flow, and she has also uncovered it. Both of them are to be cut off from their people.
Going back to the first article:
The laws of purity are indeed technically in effect; it is just that for the most part we are presumed to be in a state of ritual impurity.
So for instance, we can touch dead people without worrying about how it affects our ritual purity (x). Why then, do we still worry about touching a woman during niddah, since the mere touch would theoretically only affect our ritual purity, not incur the penalties associated with sex with a woman in niddah? Why should a husband not touch his wife in a non-sexual manner during niddah?