It might run the risk of increasing the fighter's popularity?
But, again, why is such an improvement to the fighter class so intolerable?
Most other classes have a great deal of flexibility when it comes to being able to contribute in all the pillars (I say 'most' because, while the Rogue is capable in all the pillars, a given rogue's not that flexible in how it contributes in each of them, and because the Barbarian, especially the Berserker, is prettymuch in the same boat as the Fighter).
It's not necessary in my opinion. It's always been part of the game and nobody I've ever encountered in actual game play has an issue with it. That doesn't make changes "intolerable" just unnecessary because it's so incredibly simple to address.
You asked for ways to improve the fighter. I gave an option. Your turn. What would "fix" the fighter for you and why is my solution "intolerable"?