What you'd want, at least, is a standard CPUID identification and range leaf at the top. 256 leaves is a *lot*, though; I'm not saying one couldn't run out, but it'd be hard. Keep in mind that for large objects there are "counting" CPUID levels, as much as I personally dislike them, and one could easily argue that if you're doing something that would require anywhere near 256 leaves you probably are storing bulk data that belongs elsewhere.
Of course, if we had some kind of central authority assigning 8-bit IDs that would be even better, especially since there are tools in the field which already scan on 64K boundaries. I don't know, though, how likely it is that we'll have to deal with 256 hypervisors.
I agree completely, of course (except that "what hypervisor is this" still has limited usage, especially when it comes to dealing with bug workarounds. Similar to the way we use CPU vendor IDs and stepping numbers for physical CPUs.)