However, crypto coprocessors would be a tremendously disruptive solution: we'd need to build mountains of scaffolding to allow switching to and off these cores, and to share memory with them, etc.
Even more critically, you can't just move the RSA multiplication to those cores and call it a day. The key is probably parsed from somewhere, right? Does the parser need to run on a crypto core? What if it comes over the network? And if you even manage to protect all the keys, what if a CPU side channel leaks the message you encrypted? Are you ok with it just because it's not a key? The only reason we don't see these attacks against non-crypto code is that finding targets is very application specific, while in crypto libraries everyone can agree leaking a key is bad.
No, processor designers "just" need to stop violating assumptions, or at least talk to us before doing it.