I use a pet fountain for my cat and 2 dogs. They love it! We have the Dog H2O but there are lots of cat-specific brands too.

The cat may not die from dehydration, but it can develop kidney and other issues due to less-than-optimal hydration. It happened to my cat when I was a child (another faucet drinker). Many cats prefer moving water and will drink more than the bare minimum if they are given access to moving water. The fountain has been a great solution for my current cat (and we got a big fountain because the dogs are big fans too).

IMO a faucet is not ideal the cat unfortunately will not live forever and the faucet will. But those fountains are awesome friends of ours just got one and the cat loves it and was always a faucet drinker in the bathroom.

We also had a faucet drinker and the cat water fountain solved the problem. The other cats we have had couldn't care less. As the earlier poster said, some of them just prefer running water. The cat water fountain recirculates and filters the water so you're not wasting water.