I disagree with every bit of this.
Okay so...I don't really know what to do with that then.
It's explicitly the case that 5e turned various features, both semi-mundane (hunter's mark) and openly supernatural (eldritch blast, non-Hexblade hexes) into spells. It also emphasizes rather strongly the
use of spells; there is no class in 5e that does not have a spellcasting subclass, though the Barbarian only barely makes the cut. That is, Ancestral Guardian Barbarians can cast augury or clairvoyance once per short rest, with Wisdom as their spellcasting ability modifier. The only classes which do not have spells inherently baked in are Barbarian, Fighter, Monk, and Rogue, meaning the vast majority of classes in 5e are inherent spellcasters (Bard, Cleric, Druid, Paladin, Ranger, Sorcerer, Warlock, Wizard, outnumbering the previous set two to one). Of them, more than half derive the majority (or even entirety) of their powers from spells or mechanics directly tied to spells and slots (Bard, Cleric, Druids other than Moon, Sorcerer, Wizard, and arguably Paladin as well due to Divine Smite being spell-powered). And that's excluding the Artificer, another spells-primary class. (Heck, they even tried to make a non-spell psionic class, and eventually abandoned it.)
5e is a game where spells are the primary and default means by which player-character supernatural powers are expressed. Many things that did not need to be spells were offloaded into spells, rather than being their own mechanic. This has gone hand-in-hand with the ongoing issue D&D has had since
at least 3rd edition, where spellcasting simply trumps non-spellcasting solutions, while also being easily regained, breaking the intended cost of such tools, on top of making it so (for example) it is, formally speaking, a house-rule to allow a non-spellcaster to create magic items, because
only spellcasting can do that.
4e tried to break that wheel entirely and people got some twisted knickers over it. So 5e has brought it back, and we've ended up with a new version of the same problem (though, admittedly, for new reasons). That is, the 5MWD remains an issue. People do fewer things per day than the rules were designed to expect. This shortchanged any classes built with an expectation of a long day, and supercharged classes built on spells: yet again, showing (regardless of intent) that if you want supernatural power, the thing you want is very specifically
spells, not merely "magic" or whatever else.
As for the usage thing, I'm not sure what there is to argue about. I've seen it first-hand all over the place. People say "magic," but almost always they
mean "spells." And even the rules are not consistent;
counterspell and (despite statements made earlier!)
dispel magic are
only for spells, but
antimagic field is everything "magical"--unless the effect is "created by a deity" (not clear what Cleric things that would cover) or comes from an artifact.