But that's exactly what I'm saying.That's not correct. The sources of magic "thing" also exists to give the multiverse verisimilitude. Having information about where magic comes from adds to that.
You also have the ability to create a setting where those "hard rules" don't hold true. World building is a great thing.
The "source of magic" is just a way to have every class, every feat, every item, every setting, and every species.use the same set of magic effects.
Why does the wizard, elf, and magic stick shoot the same ray of fiery fire. Because this setting uses a source of magic and it contains the same spells as this other source of magic.
If a table or DM wants to use another set of spells they have and get rid of the "source of magic " it's on them to do the work to make it themselves or buy it from someone else like in Pre5e.
WOTC didn't have a whole lot of confidence in 5e originally and made a lot of shortcuts.
The Multiverse thing came later.