I always viewed "magic is a science" as being the default D&D style because Farmer Jim can scrape up enough gold to send his daughter to the "Mage Academy" and she can learn to cast soells.
There is no special something a being in the 5e universe has to have in order to be magical, which is actually a different take than a lot of other settings where "being magical" is just a trait you are born with.
Yes, that's one pathway to magic. You can also be born with it (sorcerer), pray for it (cleric), have it granted as a bargain (warlock), etc.
One thing I dislike about D&D is that magic can do anything you want it to do (where "you" is the DM or adventure author). I long for a single coherent "theory of magic" that all magic has to work within. (Discussion about this in another thread somewhere.)
Not that I would actually change D&D, because then it wouldn't be D&D. But one facet of my non-existent dream RPG is that it has a really cool explanation for what magic is, where it comes from, how you harness it, what it can do, who can harness it, what the consequences/risks are, etc.
(Another facet of this imaginary RPG is that the vast majority of adventurers/heroes are non-magical, and the reason this is so is somehow tied to the game system.)