
Sounds like The Primacy of Magic is and important part of the Essence of D&D, for you, at least.
It's funny, these discussions often seem to get caught up on choice of label.
"Omnipressence" would work against the concept, making magic feel mundane/fungible (like magic items in 4e).
"Magic Dependency" would work fine, it gets the idea across. But, frankly, Primacy sounds cooler than Dependency, and doesn't connote addiction.
Prettymuch, yeah, it's worth recognizing that. Magic is more critical to the accomplishment of goals, even to survival, than non-magical contributions, which are fungible. You could use a shield golem or a series of conjured monsters or, at very low level, a well-trained attack dog, in place of a fighter a lot of the time. Wouldn't be /as/ good, might even get you killed once in a blue moon, but generally, the fighter's contribution is less unique, less critical, more fungible.
"Magic Dependency" would include the same information - success doesn't /Depend/ on the Fighter's contribution - but with the connotation of D&D being 'on magic' like it was a drug.
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PYL
It'd be hard to picture a "really D&D" implementation of the game in which the players of casters choices weren't more and/or more important than those made by the players of non-casters. Subjective opinions about the desirability of more and/or more important choices notwithstanding.
(That is, one could feel that fewer choices is simpler, less important choices is liberating, that his fighter or barbarian could charge heedlessly into combat, pick a weapon for cool factor instead of dpr, and generally do what he wants, how he wants it, without everyone screaming that he's not doing exactly the right thing at exactly the right time.)
Your experience is one thing (which is fine - someone has claimed exactly that experience in every edition, even 3.5 regardless of Wizards being Tier 1 & Fighters Tier 5), the implementations of the various classes in the books are another, which, is subject to examination an analysis.
Fighters, in 5e, were designed to be simpler than casters, this was explicitly stated in the playtest (with BMs designed to be a bit more complex for the sake of complexity). That design intent did not fail: at chargen & level up, in each adventuring day, and on every round, the wizard has more choices to make than the fighter. Since a lot of those choices are about whether & hot to expend daily resources that could have encounter-swinging impact in any pillar, while the fighter's are mostly about which enemies to attack in what order (punctuated by whether to Second Wind or Action Surge this encounter or save it in case there's another before the next short rest), or what mundane task to lend his stat bonuses to out of combat, it's not unfair to say the wizard's choices are more difficult, and more significant, as well, even though it's possible, depending on circumstances, that it might turn out that attacking the red monster before the green one saved the party, while casting fireball, instead of moving & casting lightning bolt, to kill both of them at once made no difference at all.