I don't know if it's really ultimatum but we have had these discussions where I've said that I'm not sure there's point to continue treatment with him because he is not X or is not doing Y. Those X and Y things have always been very subtle though, not concrete things like responding to emails.

My T has never steadily responded to emails but he also declared at one point that he would not respond at all and some time later that he even would not read my emails anymore, these events initiated many heated discussions and accusations but not the ultimatums per se.

Having feelings stirred up during the session and left to deal with them on your own is very difficult. Have you been able to talk about it in session? Have you asked him what he suggests you could do in such a situation? In my opinion, one thing that could help would be more frequent sessions. Another thing that could help are short phone calls. Not every T can accommodate that but that was something I negotiated with my T for a period where I felt that I'm just not able to get through the day. Sure, he took this option away when he figured that I don't really need it anymore and then I was angry too but in fact I truly did not need it then anymore and that was ok.

Regarding such T's behaviour as rigid I'm convinced those who see it like this just lack the wider context to adequately evaluate things. This is the same as me evaluating other children mothers in childhood. Because I had absolutely no idea what function or meaning a mother has to a child and I could only generalise from my own very biased experiences I assessed them based on beauty. I could not understand how some children could tolerate or even seem to like their not so beautiful (or even worse, fat) mothers. I just couldn't understand it back then.