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There is an event that, with a certain risk, can raise your current Magikarp's maximum level by 1.

The more I think about it, the the more short term any possible benefits of the raised max level seem to be. It doesn't carry over to the next generation, so it'll be just as slow. It'll infact take me longer to get the benefits of going to the next generation.
Even in the current generation the only benefit I can think of is a longer run in the League. This might give more money (or it might not), but I fear that even this is balanced out by the delayed next generation.

Is there any benefit beyond the current generation to raising the level cap of a single Magikarp?

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Raising your Magikarp's max level increases its JP cap, which means it can get farther in league battles. The farthest battles will get you the most coins and experience which means leveling your trainer or upgrading a training item when you may otherwise not have been able to. This is especially the case when you realize that the trainer XP you gain after retiring is tied to the level your Magikarp reaches, which means you may level up after retiring one generation early, giving you the permanent level cap increase you're looking for.

Yes, it will take longer to reach the level cap, but the 10% bonus in JP gain is quite a small relative bonus after a few generations, so it's better to get the coins and experience now rather than taking the time to raise a new generation to the same level cap.

Spoilers for those who are unaware of the risk of this event:

In addition, I would argue that it's also occasionally a benefit to have your Magikarp forcibly retired. "Macho Karp" only happens after losing a league battle, so it's likely that you've exhausted your current resources and retiring your Magikarp can level up your trainer which refreshes your training points for your new 'Karp. This can even be done before the 7-training minimum which is usually required before manually retiring. Also, there's an achievement for having several Magikarp forcibly retired which rewards diamonds and is generally harder to achieve than the "retired at max level" achievement.

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