This is the obvious way to do consensus, that doesn't work because of the massive amount of bandwidth needed to have a vote for every bitcoin address in existence. Keep in mind everyone needs to do this checking too. The entire point, and clever part, of bitcoin, is the idea that one can trade bandwidth/digital signatures for CPU-intensive "hash signatures" that are very small and easy to verify.
In other words, if you asked someone to design a system like bitcoin before bitcoin came out, what you propose is what most would have said...
Haha, I thought it felt a bit too obvious. Well at least I have a greater, more justified, appreciation for Bitcoin now.
This whole thing actually came from thinking of a way to solve the checkpoint problem Ben Laurie wrote about. If votes don't need to occur very often, then would the bandwidth/checking cost be such a big deal? Is his issue even really a problem?