A bad idea
Like any substantial change to the existing semantics, this is going to break a lot of things. Exception handling is one prominent example: any code relying on the old-school setjmp/longjmp will be buggered. Fixing it would require compiler modifications and complete recompile of each application involved, including the libraries. Even then, there might be corner cases which won't be fixable. One might think of fixing this in an exception handler, but my head starts to hurt even trying to think of how to deal with the recursive routines.
At this point in time, x86 has become a horrible mess of warts, some of which have warts of their own. Adding yet another level of complexity will further decrease the number of people who actually have an idea of how the whole thing is propped up - and it is already tending to zero as it is.