I have never seen a game do this either. This is how I would design it so that hopefully there is an incentive to level up:
At the beginning, when the character is young, they will be able to use the brute-force method. The character will have no issue wiping out waves of low-level grunts. The issue arises when the player encounters more intelligent enemies who can avoid or outsmart these simple attacks. The player has no means of fighting them because they aren't smart enough.
As the player ages they will no longer have the strength they once had. However, they will have gained wisdom, which will allow them to outsmart those highly intelligent enemies. In fact, when speaking in terms of potential, the older player can be more effective. Strategy is more powerful than brute-force.
In this design, enemies don't become much more powerful, but they do get smarter and smarter (which possibly means better AI).
Here, the wisdom stat is your magical power. You might be able to turn this into something other than magic, but the same basic idea applies. Slowly degrade the players strength but slowly reveal to them new dynamics of strategy.
This design gives players an incentive to level up, even though they will degrade other stats. This will also increase the level of challenge throughout the game because it gradually forces the player to use more intelligent strategies.
So, to answer your question: The downside to this (well, not a downside, just a challenge) is you have to be very clever with how you intend the player to use strategy. You have to design it in such a way that the player must use strategy to advance. You have to design it so that the ability to use strategy is more desirable (and more satisfying) than the ability to use brute-force. You have to make enemies intelligent as well (or make them seem intelligent while simply having puzzling loopholes in their defenses), which is obviously difficult to pull off.