Well, in software terms, you're describing a monolithic architecture. A single cavity would destroy the whole thing. You'd probably have to replace the choppers more frequently as your skull grows into adulthood, or we would have to be born with larger jaws that don't need to grow as much as we mature.

There is also the matter of how evolvable the platform would be. As a species, we're in the process of losing our wisdom teeth, and I suspect that would be harder to do if the skull/jaw/gum/tooth platform was... more tightly coupled, less modular.

I myself never had any wisdom teeth, and kept a couple of my milk teeth into my 40s before one had to be replaced with a crown, and the other just fell out when the root dissolved. Human dentition has a lot of variability.

Still, birds did it (as have other species over the Earth's long evolutionary history), so it isn't an insoluble challenge, but it would be a rather more radical change than just fusing teeth together.