There's nothing stopping you from giving each stack its own IP, making the kernel only responsible for routing.

I don't think it's a good idea to put more of the stack than necessary into each individual program though, because then you're reliant on each program implementing everything correctly and you have to worry about bugs and security issues in every single program you're running rather than just in the kernel.

Considering that even something as simple as opening a socket (which involves calling one function to give you three numbers which you pass unchanged to a second function) is largely a clusterfuck in existing programs, I don't trust them to implement the whole TCP stack.