The biggest problem is when you tie important aspects of the class's power to higher ability score.
In 5e, the number of spells you can prepare, as well as the Spell DC/to Hit, is partially governed by Intelligence. In 4e, it was spell rolls. In 3e: not only was DC determined, it was a factor in starting spells known and bonus spells. In AD&D, the number of spells you could learn, max spell level, and chance to learn spells were all governed by it. In Basic: you got a bonus to your Xp.
In every edition but Basic, high Intelligence literally defined how good a wizard you were. The gulf between a 13 and a 16 was massive: it determined how hard your spells were to resist, how many you know, and even how often you can use them. In Basic; it was 5% xp. Every edition but Basic all but demands you put your highest score in Int and do nothing but improve said score (either because it would become a roadblock if you reached high level without an equally high Int score or because the monster/save math demands you max your saves/attack). Basic just meant you'd level a little faster.
If D&D returned back to decoupling raw spell power with Intelligence (for wizards, replace caster stat as appropriate for other classes) you wouldn't see the raw dash to get 20+ Int scores as soon as possible. And I think that would be healthy for the game. But I don't suspect people are quite willing to have Int be a minor or non-factor in spellcasting just yet...