What's a better story, that everyone can learn magic or that only a few can? Depending on the setting, I admit that it can be either. Darksword trilogy was a world where everyone could which made the one person who couldn't stand out.
In many stories, magic is rare and special, you don't see everyone casting cantrips or spells to make their life easier, rather you have a single magic-user in the town, maybe they're the only one in the entire region, other than any PCs that have learnt magic. It is my preference that this is the story behind magic. There might be many ways to learn it, but every one who does has the spark of magic within them, they're special in some way. For PCs, they're always special if they choose feats of multiclass into a magic using class, I don't limit players, if they pick up the skills then they had the spark of magic. I just prefer that for world building, magic is a rarer commodity that not everyone can learn.
I don't know if you know much about Mystara, but the empire of Alphatia is built upon this story element. Once a highly magical people, the number on magic-users has dropped considerably because not everyone can learn to cast spells. I like that setting element.
I should note that in my setting, some races are highly magical. Dragonborn as a race are almost always able to tap into their draconic nature to become sorcerers. Humans, however, might not be able to learn magic no matter how long they study.