As a (very) rough sketch to show you what I want and what I think would serve the game MUCH better, would be to scrap the existing rules entirely and instead base a new set of rules on "stances", and for each stance define what actions are restricted or outright impossible, with the notion that anything not specifically limited is okay.
Also, a ruleset that much more defers to the DMs rulings and common sense, rather than trying to be exhaustive.
Something like this (again, a very rough outline, more meant to steer the thread than to be a complete proposal).
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At the start of each of your turns, you decide upon a stance (see below), which you are assumed to remain in until the start of your next turn. There is no cost (in actions) in switching stances, except when you switch into or from a shield stance - to do this you need to spend your action on the don/doff action.
One-handed stance. Example: you wield a Longsword with one hand, having the other hand free. You can't benefit from a shield. You can cast spells or you can hold a lantern or you can manipulate one object (choose one each turn).
Shield stance. Example: you wield a warhammer in one hand and wear a shield in the other. You can cast divine spells. You can't hold a lantern, cast arcane spells, or manipulate objects.
Empty stance. Example: you hold nothing. You can cast spells, hold a lantern, manipulate one object, and manipulate one more object (choose any two each turn). You have no threat range and can't make Opportunity Attacks unless your unarmed attacks deal more than 1 damage. You can spend your action to don a shield, turning this stance into a shield stance and reducing your choice to one each turn.
Two-handed melee stance. Example: you wield a Greatsword with both hands. You can't benefit from a shield, you can't cast spells and you can't hold a lantern or manipulate objects.
Two-handed ranged stance. Example: you wield a Longbow with both hands. You can cast spells or manipulate an object. You can't benefit from a shield, and you can't hold a lantern. You have no threat range and can't make Opportunity Attacks unless your unarmed attacks deal more than 1 damage.
Two-weapon stance. Example: you wield two shortswords. You can't benefit from a shield, you can't cast spells and you can't hold a lantern or manipulate objects.
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Simple huh? That might actually be it - EVERYTHING you need. (I might have forgotten an obvious stance, remember this is rough)
Don't worry about the details - the main point is that the 5E rules could have been VASTLY more newb-friendly and fast and simple!
Do note a little polish is probably needed. For instance how "you hold nothing" allows "cast spells" - this assumes you can grab your focus that turn (if you use a spellcasting focus or have otherwise found a magic wand etc). Holding a "lantern" is obviously not meant to exclude torches or your adventure company's banner (or whatever). "Manipulating an object" includes everything from sheathing a weapon and pulling out a scroll from your gear to picking up a key from a table or locking the chest with the key.
Hopefully you will see how the focus is on what you do during your action, not how you got there. Switching between stances implicate drawing and sheathing just the right amount of gear without needlessly making you worry about it.
Then you might add a few bits and bobs. I'm mainly thinking of differentiating between spells with and without material and somatic components. You should be able to cast spells with neither even if you made another "choice" (such as holding a torch). We probably need give Bards two seconds of thought.
It's important to me that we analyse the rules we end up with so the BS move "drop weapon cast spell pick up weapon" is entirely impossible.
The rule "you can use the same hand for both material and somatic component" is assumed, since we say you can cast your spells with one hand free, so no need to get that complex.
Focus-less spellcasters (such as Arcane Knights) are shafted, but then again, so they are in the core rules (I think?).