The problem is that you have to have a monitor plugged in the windows card otherwise it goes all wonky. At that point you could just use a KVM....
As a sibling comment stated, you can get a dummy monitor plug on Amazon for like $5 which fools your GPU into thinking there's a monitor attached.
In nutshell, KVMs aren't worth their money because they have to re-implementing a lot of hardware already found in your PC.