The most common case I’ve hit issues is the remote server is down or blocked but the connection hasn’t yet terminated so exit is no longer possible.

I've occasionally had things crash in ways that have swallowed ctrl-c. More recently I've learned to still try ctrl-z in those cases, as that often still works (but not always).

None of this is very common, but I found myself opening another terminal and killing the ssh process probably tens of times before I learned about the ~ escapes.

Yeah, that's the only time I've had to use the escape sequences. However that happens to me only once a year or so (but maybe I don't use ssh as often/in the same ways as others).

I guess my timeout is really low, so it’ll fail fairly rapidly.