That would hardly be writing a new protocol - you could do that and keep compatibility with ActivityPub entirely. You would just need to clarify and add some stuff to ActivityPub. This would basically be ActivityPub 1.1.
I think this is also a bit backwards - the protocol should define how things should be done, not the other way around. How things are currently done should not necessarily dictate how things should be done (how things are currently done might just be popular but suboptimal (tbh this is exactly the current situation)).
But an AP 1.1 would not fix any of the problems with the protocol that cannot be fixed in a backwards-compatible manner. One of the biggest issues I’ve seen in that category is the inability to change AP implementations on the same domain, just to mention one thing. But there are others.