All versions of D&D, even first edition had super natural and unrealistic powers that where by definition of the game "not magic" but had similiar or in many cases exactly the same effects as actual spells. 4e was not unique in this by any stretch of the imagination.
What 4e did was effectively take movie scenes and turn them in powers that could be executed, every martial power in the game you have seen enacted in a movie somewhere and in most cases it was not magical, it was simply cinematic. 4e was really good at giving characters the ability to act out interesting scenes within confines of the rules, but through vivid and very specific imagery. Something that in all editions of the game as players and GM's we strive for anyway, it was just done outside of the confines of the rules.
For example if you wanted to kick someone to stun them before you struck him with an axe, in 4e there was a very specific martial power that did that, to that description. In AD&D, 3rd or 5e, you might describe your action (stun kick) and the GM would be expected to find a way to resolve it, but within the confines of the rules you would be reaching for general rules like "the golden rule", "DM ruling power" or some general rule that covers stunning someone to define how that is resolved.
I think the issue was for many D&D players is that they believe (as I do) that the latter is much better. It opens up the game and doesn't require you to explain yourself when you do it. What I mean is that if their is a martial power (stun kick) in 4e that very specifically defines what it does, how it looks and what it is. If the mage tries it you are stuck in a wierd place because kicking someone before striking them with an axe isn't really a power, its something anyone could try. Rage, Favored Enemy, Divine Smite... those were powers. 4e had too many mundane things it considered "powers" which were really just a combination of actions I would expect anyone to be able to take. The issue you ran into was when someone actually did. For example a mage tries to kick a guy to stun him and then smack him with an axe. Perfectly reasonable and your stuck with this wierd resolution, do you resolve it as the Martial Power, or do you "GM invent it" because there aren't any specific rules that handle that sort of thing other than "rule zero". At which point you have to ask does the world really make sense now... is the Fighters a magical stunning foot? Is he stronger? What if the mage has a strength of 17? Is he better trained at stun kicking people.. .is that really a thing?
For me this is kind of the place where 4e kind of fell apart, in particular when you layered it with all this tactical movement shifting all the time. It created bizarre scenes that didn't really have a sense of place or logic even in a fantasy world with magical spells and dragons.
It just didn't work and I think this is one of the many elements of 4e that lead to its wide scaled rejection from the player base. Its not so much that it was a bad system but between 1st, 2nd and 3rd edition, we kind of had this figured out already, it really didn't need to be re-invented.
Its worth saying to that 5th edition in particular handles "invented actions" better than any D&D system before it. You have the advantage system, skills, proficiencies and feats. You can always explain things logically by pulling from those resources during a session and I love that. In partiuclar the advantage/disadvantage system... I love it so much, so simple, yet such a powerful roleplaying tool.