There have been attempts to move the register renaming out of the processor and into the program through VLIW architectures such as the Itanium, but it failed because (1) they require “sufficiently smart compilers” that weren’t available in the day, and (2) putting it in the silicon allows new architecture revisions to benefit older programs (putting it in code means it can’t benefit from newer register renaming algorithms without a recompile).

Also, if it’s in the silicon and there’s a bug in the algorithm, a microcode update can fix it for everyone. If the bug was in the compiler, you’d need to recompile everything to fix it.