What you describe could be done, but it would be difficult to implement, require special compiler support to do well, and would break source compatibility even with special compiler support.
It would be essentially the same as adding support for 80286 style near and far pointers across the code base. In C, every structure, every header file, every shared pointer declaration would potentially have to be marked whether it was using large or small pointers. The compiler certainly wouldn't know that an arbitrary function or structure declaration was referring to something from a library, and some libraries would have to come in a non-standard flavor in any case.
Now as you say, there are certain advantages to that, in terms of memory and cache footprint. They did it back in the x286 era for a reason. But it is much more impractical to implement that sort of thing across the source code for practically everything then simply to compile under a new ABI, especially if the new ABI performs well enough to be the system default.
A reasonable distribution policy could be to replace x86 with x32, and not ship x86_64 libraries in x32 distributions. It could simply say that if you want have a 64 bit user space, you should use a full 64 bit version. 64 bit addressing could be reserved for the kernel. If I were to guess, half of the people currently planning to use x32 (e.g. in embedded applications) have that sort of thing in mind in any case.