Well, perhaps. But If we pursued this, I think we would want to adopt a standard and commonly used system. For example, the system I have seen used most frequently in genealogy publications is the Modified Register System. I haven't personally used it, but it appears to have a bit of complexity, and a learning curve climb, associated with it, and I'm not sure that mixes all that well with researchers who don't have much experience.
The other issue is that this is a dynamic tree that will never be finished, and more ancestors and more descendants are being added every day. It would be a real problem if some of those additions dicated a renumbering exercise, and I don't think any of us would want to see that. Erin mentioned one name studies, so perhaps the idea is to somehow partition off small sections of the tree that are basically complete, and that could use a numbering system within a bounded group of profiles. Perhaps a workable concept for that could be developed, but again, I'm just not sure what the purpose is.