If you play through the B and X series of adventures, they are quite low magic. Yep, there may be a huge group of 36th level wizards but you're running against lower powered threats. That doesn't mean you won't eventually do so, but for a long time, those levels didn't even get support in the game.
I guess the problem is, different people mean different things by these terms.
"Old school" low magic: Average peasants might doubt magic exists. Even if you know it does, you probably don't know any magic-users, except (
maybe) a local priest with weak healing magic. If archmages exist, they start out far away and rarely matter to most people.
"Old school" high magic: Most people have observed magic practiced, and usually know someone who can use magic. When feasible, magic is used to enhance daily life and economic productivity. Most major cities will have at least one practicing archmage, possibly several.
"Modern" low magic: There literally isn't much magic
at all in this world. What magic exists is generally feeble, or only capable of significant effect with a lot of preparation time. Few if any archmages
have ever existed, and it's unlikely that any exist currently.
"Modern" high magic: Extremely powerful mages exist and may even rule entire countries. Magic can do incredible feats, and even if it isn't the most accessible thing, most folks know that magic exists and have a rough idea of what it can do.
That is, the "modern D&D" idea of "low magic" has been pushed down to near-zero, something more like Conan and Cimmeria, while that of "high magic" is more about cultures and potential than about actual daily practice per se.
...actually, maybe that's a better way to phrase it. One is social-status-focused (old school, asking "what do average folks
see?") The other is
cosmology focused (modern, asking "how
powerful is magic?") By the cosmological standard, almost all old-school settings are high magic, because archmages are real and in many cases rule entire countries and do massive stuff with magic: it doesn't matter that few
do go into the study, those who do gain great power. By the social status standard, almost all modern settings are high magic, because magic is a well-known aspect of life for everyday folk: it doesn't matter that most magic-users might be only hedge witches, if
everyone knows a hedge witch.
Ironically, even though the social status standard is the old school one for D&D, it's actually the one much closer to modernity, a product of the Enlightenment's empirical project. The cosmological standard is much closer to Antiquity and the pagan aspects of the Medieval Period, because the average Roman or English peasant
knew magic existed and, at least for the former, we have conclusive proof that they practiced this magic on the regular (curse tablets, engraved gems, mystery cults, etc., etc.)