You appear to not understand how password hashing works. A well designed hashing function is one-way, it cannot practically be reversed. With a large salt, even very weak passwords ("cat") cannot be reversed.
Not only that, but the size of the "salt" has nothing to do with how long it takes to brute force a password. We should stop saying "salt" and start saying "randomizer" so at least people understand what that thing is doing; I think everyone understands intuitively that a hash can be "randomized enough" so that further randomization isn't a win.
And you'll still be able to brute force "cat" in under a day.