You're talking about rainbow tables. They aren't used very much anymore, since the salting of hashes has become commonplace.

As for your idea that hash functions can't be reversed, not so much. They can't be easily reversed, but that's not the same thing.

In reality, brute forcing is pretty much the only viable attack left now that salting is commonplace. Still, if you have managed to get your hands on the password table, you can brute force without having to worry about rate limiting etc.