For the most part I can agree conceptually what you are stating here and for you and probably others it works. But I'll say this for me personally... because all classes in 4E were on the AEDU format and all powers encompassed the exact same suite of grid tactics (adjacent damage, blast damage, burst damage, pushing, pulling, marking, knocking prone etc. etc.)... any so-called "non-magical" classes in the Martial power source did almost the exact same kinds of grid tactic actions that the so-called "magical" classes did.
Which means that at least for me I never felt any real difference between magical and non-magical powers other than the Martial power source not having ranged burst (AoE) attacks. Everything was just 'Move here, attack this/these creatures here, move those creatures over there, shift here' and so forth. None of it felt really different, even though we were supposed to identify certain ones as "maneuvers" and others as "prayers" or "spells". "Low-magic" campaigns and "High magic" campaigns did not exist as separate things, because for me the tactical board game felt the same both ways at the same time.
I do not doubt that other people did indeed conceive all of these powers differently and actually felt like maneuvers were different from prayers were different from spells. But unfortunately some of the rest of us did not. And that's possibly one of the reason why 4E maybe ended up being more divisive in certain circles than I bet anyone thought it originally was going to be and perhaps trying to recapture some of that 4E essence in 5E wouldn't actually solve the problems that people might think it would? (And not suggesting that's what I think you are saying, because I know you're not making that case.)