Hey I’ve just had a crazy idea about magical strength to do with the whole wands being used to restrict magical output thing?
Ok so if we run with the idea that magic is like a muscle, that needs to be flexed to gain strength and grow etc and that wands are like levers lifting buckets of rocks whereas without a rock you lift each rock yourself then what if magical strength is partially (but as Neville will prove not wholly) due to how much magic you use as a child.
Magical children in magical families don’t need magic so much, they know they are at least likely to have it and being aware of it they would be less likely to produce accidental magic.
Then you get the muggle-borns. Muggle-borns which are noted to often be more powerful (see Hermione Granger, statements made by assorted teachers). We know that both Harry Potter and Tom Riddle were flexing their magical muscles when they were very young and both of them grew up to be incredibly powerful.
Of course sometimes you get counter-examples, like Neville listed above, who seemed to become more skilled when he got a wand that matched him, rather than his dads old one. This would suggest that some magical power is inherent in the person - Neville is a naturally strong Wizard, as, most likely, were Dumbledore and Grindelwald.
But if magical strength is grown by using accidentally as a child then that might explain the strength seen in muggle-born and muggle-raised students.
(also sudden side-theory - what if non-verbal magic, which we know Dumbledore to have been skilled at, also helps grow the magical muscle so to speak, which is why Dumbles is so INSANELY powerful, and thats why casting non-verbally is hard because you are stretching a muscle most wixes haven’t used, and those that have flexed it before won’t entirely understand how, which is why its so hard once they learn to attach magic to words, rather than instinct and ideas)
essayofthoughts has some fabulous ideas here that I’m going to build upon:
I think we can work around the Neville example though if we go with the idea that magic is inherent - how people manage to bring that magic out/express it is not.
So the expression of magic would be a muscle so to speak? Or will/intent? So muggleborns, because they’ve never grown up around magic before and because they’re in an environment where using magic (accidental or otherwise) around other people will get them into trouble - after they’re of age for Hogwarts - they grow used to learning how to intentionally control their magic, consequently learning how to channel their magic far more effectively than purebloods who do not have such punishing consequences!
Like in addition to muggleborns being adroit with the use of magic, we also have pureblood & half-blood figures like the Weasley twins + Ginny Weasley, Lupin, McGonagall and Snape who are all exceptionally talented wix. I think the unifying factor here would be the fact that these are all intellectually curious characters - i.e. fond of playing around with and experimenting with magic, or generally intellectually well versed with the theory of magic etc. Which leads me to believe that it’s more a case of mind over matter so to speak - intellectually curious people fare better in learning how to handle their magic, which would explain ALSO why Hermione and Tom Riddle Jr have managed to develop their magic to the extent that it is constantly remarked upon by other people as something curious to be marked.
Also, idk if this is canon or fanon, but I like the idea of pureblood kids being exposed to wand magic as the normative magic at a younger age and being given illegal wands at a younger age (I double dog dare you to tell me that Draco didn’t have one of these, spoilt little brat that he is). So I mean, they’re literally being brought up to rely on this crutch, this lever as you call it (I really love that metaphor bc it just fits so perfectly), to do all their channelling of magic for them rather than learning to will things into happening.
I think this also wraps in your headcanon about Dumbledore and non-verbal magic which is absolutely spot on - non-verbal magic would depend more on the wix’s ability to exercise their will than on their ability to wave a wand in a particular way and say a set of words in a particular way.