Rapid tooth replacement has certainly worked for sharks. In fact it might even be that the genes for rapid tooth replacement in sharks and dinos are the same. The book “Endless Forms Most Beautiful by Sean Carroll points out that genetic material is frequently reused—like the mammalian spinal cord, the segments of insects and the segments of earthworms.
Regarding the method of using teeth. I just read Jurassic Park (somewhat different than the move and very interesting). There it was hypothesized that herbivore dinosaurs were using gizzard stones to grind up their plant food. With their relatively small heads biting and chewing just would not have accomplished enough nutrition. Chomping and swallowing would be much more efficient.
We have a washout over on the big ranch where we find lots of teeth everytime it rains. They average 2 to 3 inches long and 3/8ths to 1/2 in diameter.