It doesn't seem to me that calling the address "noreply@" adds friction. It does seem to me that calling it "mail@" encourages your customers to put messages into a bin that has to be manually sorted by a person/team with limited resources, which may potentially increase friction.
It goes without saying though that regardless of the name, you should still have somebody checking the inbox.
noreply@ adds friction because it doesn't invite to communicate. I don't know about you but I, for myself, want to communicate with my customer to get feedback as fast as possible. 2 real life example:
* I once sent a email to my customers about an upcoming maintenance window informing them that our platform would not be available for a certain time period. I got one customer quickly replying "next time, please let us know 1 week ahead" Point noted. Now I send my maintenance notice 1 week ahead. Happy customer.
* We have this automatic billing system which sends an invoice through email following payment. I had a customer once replying saying "Hey. That amount should be x+y instead of just x". Point noted. Shit happens and I wanna know.
Yes those customers could have reached us through our website or something but my point is, why not offer them the chance to hit reply? It's so close!
Also, If you don't have a good ticket system to skim through those incoming replies quickly, maybe you should get one. It pays back rapidly.
It goes without saying though that regardless of the name, you should still have somebody checking the inbox.