Most fantasy Wizards can do anything unless they can't, lol.
Even if they claim to not be able to do something because of "da rulz", you can be sure someone in the story will do something "impossible" to flex their power and style on lesser casters.
True, I will give you this. Many magic systems are not consistent or simple left vague so that someone can break the rules, or "dig deep", or whatever to do whatever is plot needed.
But they still don't seem super D&D wizard like. They may be as or more powerful than D&D wizards at times but they don't seem to be as reliable or prolific in spell slinging which is also IMO what makes the D&D wizard unique (and mostly not in a good way).
It is rarely -- meet some obstacle, throw spells at it, repeat. There is almost always some limitation that requires non spell solutions to some problems (traveling, fighting, social, sneaking, etc). And yes, it is often not well thought out and comes down to narrative coupon but it is there.
I'm not familar with all your examples but in the Belgariad wasn't there fatigue or something that prevented wizards from using the will and word at the same rate as a D&D Wiz?
And it's true Harry Potter wizards seem to be able to do spells at will. That said, the stuff even the teachers can do seems a bit limited -- mostly the same 5-6 spells. With other magic coming from potions and items. Although those don't seem to be super hard to come by either. You can't just teleport anywhere but need to go through the fireplace, you don't see everyone going invisible -- just the special plot cloak, etc
I still say its this combination of power, breadth, reliability, abundance, and no cost that makes the D&D wizard what it is and not like many fictional magic users. As pointed out in other threads, even most D&D fiction doesn't really allow for a full spell load out and use.
So where I land is either the high level Wizard should be reined in and would advocate on breadth first, or just accept that this Dr. Strange style Wizard is a critcal part of D&D at higher levels and create a mythic martial to go along with it.