Pages 58-59 of the Basic rules:Ability checks aren't solutions.
An ability check tests a character’s or monster’s innate talent and training in an effort to overcome a challenge. . . . Every task that a character or monster might attempt in the game is covered by one of the six abilities.
This tends to suggest that making (and succeeding) at an ability check is one way of succeeding at (or solving) the challenges posed by the game.
Upthread I said that the very stark division between "mundane" and "magic" drawn in 5e strikes me as an obstalce to playing a RPG of the sort I enjoy. The several pages of posts since that have not dissuaded me of that view!
I can't deny that there is a strong heritage in D&D of spells and magic items being somewhat unique in being both in-fiction resources that therefore can be managed and deployed player-side yet also mechanical capabilities that bind the GM in various ways. But in AD&D thief abilities serve as something like this for non-caster characters; and obviously 4e provided non-caster characters with a very wide range of capabilities that had that nature.
At least as you present it, though, 5e is a more orthodox version of D&D in this respect even than AD&D!