It's certainly true that for a some mathematical problems memorizing the steps to the solution is often the most practical way forward (especially if you're planning on passing an exam), but there is definitely more to it. Most of the work proving things is actually exactly what you say - going down a different route. That's why mathematicians have careers, they spend days/months/years going down different routes and taking different appraoches to solve something. Naturally, they don't explain all the ways they didn't solve the problem when they finally do solve a problem. You don't need to know the answer to get to the solution. This is just like saying "The problem with a maze is you need to know the route through it before you can get through the maze"- no, what you do is you search for the route through the maze and once you've finished searching then you know the answer and suddenly you can walk through the maze repeatedly very easily.

And similarly, whilst one proof might have limited practical applications, it's very difficult to know which proofs do have practical applications and it's almost impossible to know which results might later yeild further proofs that do have practical applications.

None of this is really a matter of intelligence, it's a matter of putting in work (although obviously there is intelligence involved to find particularly neat ways of appraoching problems).

And why do mathematicians learn proofs? Often, to see the approaches that you can use to solve other problems.