But 5e solved a lot of that with greater bounded accuracy (though there are some +5 magic items that can bring it back a tad). Your right that when your dealing with +10 vs +3....sure the bard is going to be the best, but not so good that others can't be better at the right oppurtunity.
A 35% greater likelihood of success is rather striking. In any scenario where DCs are set
independent of the skills of the character making the check, that's the difference we're talking about. Maybe you can ignore that. Good for you - but that's not a system that rewards new and inexperienced players well.
Now, if a DM alters DCs to fit the more meagre checks of some characters, that's different, but then why use a system with skills and ability scores at all?
Some characters will always be better than others at certain things in 5e, and it is also possible to put together a particularly weak character. If success in any of the three pillars matters to the player, that is going to feel like being a weak thing alongside a strong thing, and that gets old. Maybe not for you - again, good for you. Unless classes have "this class is weak at x" disclaimers in the PHB, though, it is a problem.
Further, the long standing existence of these class difference in performance in different pillars shores up the player conceptions about which classes can do which things.
5e is better than some previous editions about this stuff, but it still exists. Game balance within pillars is atrocious, and as there is no universally agreed upon distribution of game session time to each pillar, it means table to table balance is both atrocious and
unpredictable.