I think it depends with the emails. For example, I almost never got anxious about or dissected what the T might be feeling when I emailed them and also didn't wait obsessively for their response. But I very much like the idea to give (and also get, when I am supposed to be the consultant) people time to think more deeply, maybe do some research, before expressing their views and giving advice. When it comes to being upset and conflicts, I think having a bit of time to think through can be especially helpful and make things much more effective. Others may prefer more spontaneity though - my first T was like that and that was one of the many reasons we were not a good fit.