I think there is nothing wrong with asking a candidate to do live coding/algorithms given that they could be solved in reasonable amounts of time and the interviewer has practice in helping a candidate feel comfortable doing so.

If I'm in an interview and I feel judged/nervous enough I'm going to struggle to spell my own name, much less write a merge sort. If I feel like I'm having fun and the interviewer is just sort of pair programming with me to make sure I'm not BSing that I could code, then sure, I can probably do most medium level algorithmic problems after some stumbling around and mis starts.