Gammadoodler
Hero
5e Bards' schtick, as described by the game, is magic and music.Sure, if you ignore what those classes stand for. Wizards and warlocks are knowledge and power, not athletics, medicine and performance. Monks are rigorous training and self-perfection, which is physical and ki, not skills. Taken out of context, sure you could apply those things to skills. I don't take them out of context.
With rogues you would have a point, if they didn't get reliable talent instead as THEIR schtick. Only bards have the schtick of being decent at everything.
You've highlighted pretty much all the skills stuff in the class description and,
A. It's barely anything
B. It doesn't actually say that Bards are good at skills, just that they see using them as a reason to go adventuring, and
C. The experiences that they go through to learn skills are common to all adventurers.
I can accept that the Bard has a mechanical identity of 'skills person'. I don't accept that this is a well-justified core narrative identity.
Certainly not so core and singular to their identity that it should preclude other classes from having more options for skill progression.