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...