It depends a lot on how the game is structured.
The levels are there for a reason - to give the player a feeling of progress.
Games that force grinding to reach levels, and require those levels to pass obstacles, are a really bad implementation of the level concept: First because the slow leveling due to grind does not give the player a feeling of progress, and second because the requirement to have certain levels to progress the story is bad story design.
Giving more EXP to go through the levels faster only removes one error of grinding games. If you create a level cap that can be reached early in the game, you're making a similiar mistake: you're destroying the feeling of progress by leveling.
So now you propose to restore that feeling of progress by giving the player different options after reaching the level-cap.
Is there a specific reason why you would want to do that?
Because in my opinion it would be better to have the additional options available through story progress independently of level reaches - and make that story progress independent of levels as well. Several of the best games around can have the story finished before the player even comes near the level cap, simply because they don't force the player to need to be of a certain level to get through - and that is a much better way to discourage grinding, simply not needing it to pass on...