Can I use const in vectors to allow adding elements, but not modifications to the already added?

Question

My comments on this answer got me thinking about the issues of constness and sorting. I played around a bit and reduced my issues to the fact that this code:

Answer 1

Compilation fails because push_back() (for instance) is basically

underlying_array[size()] = passed_value;

where both operand are T&. If T is const X that can't work.

Having const elements seem right in principle but in practice it's unnatural, and the specifications don't say it should be supported, so it's not there. At least not in the stdlib (because then, it would be in vector).