Other animals don't do this. What is unique about sharks that requires them to regrow their teeth over and over, or what benefit does it provide them (that wouldn't also be evolutionarily advantageous to other animals)?
Actually, most animals with teeth are polyphyodonts - they regenerate teeth throughout their lifespan. This includes sharks, crocodiles, fish and some mammals (kangaroos, elephants and manatees). Diphyodonty (only replacing teeth once) is the exception. I have a vague memory from undergrad that the evolution of specialised teeth in mammal-like reptiles, and specialised jaw musculature (which happened at the same time) is/was believed to be the reason behind this - for a reason I can sadly no longer remember, tooth specialisation and tooth regeneration are incompatible. When I can find more details and a source for the latter I'll edit them in.