Well, but then you’re basically just pushing the mutability onto the container

That’s the point, when programming with immutable structures you always pass the mutability onto the enclosing structure.

It’s a good strategy at times though. Like say you’re working in a language where strings are immutable and you want a string you can change. You can wrap it in a list along the lines s=['foo'] and pass references to the list around instead. Then if you go s[0]='bar' at some point, all the references will now see ['bar'] instead.

A list is an antipattern here IMO. Just wrap it in some dedicated object (see e.g. Java’s StringBuilder).

What you need here is not the stability in memory (i.e. of pointers, which you lose when you recreate an object) but instead just the stability of an identifier (e.g. the index into a list).