@JohnSnow, I am going to ask you to delve a bit deeper into some of your points in the OP, if you don't mind? (Or anyone else who wants to chime in...

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I’ll do my best to give my answer to these as briefly as I can. In order:
What is mechanically simpler in B/X compared to 5E?
Every exception is a rule. B/X had fewer class powers, and fewer species abilities.
The hit point cap was lower. The game didn’t have Actions, Reactions, Bonus Actions, Minor Actions, Attacks of Opportunity, etc.
The munchkinning potential of finding “broken combinations” was much lower.
What do you mean by "better" to you? I never considered the NWP from AD&D as a "wing it" sort of thing, so I am curious how your experience differed?
NWP’s are insufficient to cover the breadth of a heroic character’s skills. I’m thinking of Fafhrd and the Grey Mouser, who were talented athletes and horsemen, versed in lore, both of whom had stealth and thief skills, Mouser was a skilled forger, Fafhrd was a singing Skald, etc.
AD&D basically left all but a few skills as class abilities and 2-4 non-weapon proficiencies (when those were added) to DM fiat. With no guidelines for resolving them. Zero. Zip. Zilch.
What about it did you love compared to what you already had in B/X+AD&D/2E?
Ascending armor class. Unified attribute bonuses. Skills providing a unified resolution mechanic. The codification of combat NWPs in the feat system meant Fighters got some cool stuff to do. It was a vast quality of life improvement. The cracks were all in the implementation.
How was the magic system in 3E grating (especially "still" grating)? I know you mentioned you like the roll to cast mechanic, was it just that or something else?
Spell slots is my primary complaint. It always required elaborate justification. Some of the spells are way too OP, but that’s minor.
I’ve never loved the strict arcane/divine magic divide, but I realize I’m in a minority there.
Also, the “crossbow wizard.” I have no issue giving spellcasters a weak magical attack at-will so they don’t need a crossbow. YMMV.
As an aside, my first C&C gamemaster let my wizard have two “at-will” powers: “Cantrip” (basically “prestidigitation” at-will) and “Arcane bolt” (which was a Dex-based 1d6 ranged attack). With those two powers, I always felt like a wizard, and It did not feel overpowered at our table.
d6 skills. Saving Throws. And Tables. Tables. Tables.
How do you envision creating more "fun combat options" without "fiddly rules"?
I think something like DCC’s “Mighty Deeds” crossed with Luck/Deathbringer Dice that provides revolution guidelines for what’s an appropriate effect to trigger by level.
Actually figure out simple rules for grappling, throwing, tripping, disarming, et cetera. And making tactical choices in combat.
I’m spending most of my homebrew effort on this topic.
Why aren't they "there" for you, what is lacking to make such options ideal?
See above re: combat.
Shadowdark is super-close, which is why it’s my system of choice.
Characters are a little too fragile (easily fixed), it doesn't have a skill system, and it lacks those combat options (although it does use luck tokens). It’s also a bit obsessed with niche protection.