Does session management really belong in the terminal emulator?

to answer that question we need to first look at the alternatives. whee else could session management go? and then we can consider the benefits and drawbacks of each approach.

if you are thinking of tmux then the problem here is that tmux is in itself a terminal.

to get session management away from the terminal it would need to be done in such a way that when the session tool connects the session it merely acts as a proxy or less, but does not interpret and then translate the signals that come from the session like tmux does.

this is not trivial, at least with the current way terminals work.

we need to entirely rethink the terminal protocol: https://news.ycombinator.com/item?id=47941354

I‘m not sure I understand the question. Some people use similar kinds of sessions in terminal multiplexers such as tmux (is that what you have in mind?), but this leads to problems (interpretations of key sequences, etc.) that the Kitty solution sidesteps.