Actually, I'm playing a role-playing game the way they've been played for decades. In every RPG I've ever played, the rules correspond to specific in-game elements. (There are a tiny handful of exceptions, such as XP, which very seldom come up during actual play--XP is mostly used during chargen and between sessions, not at the table.)
So your in-game characters only literally ever perform a single action and move every 6 seconds? There's no parrying, fancy footwork, ducking, lunging, jockying for advantageous terrain? It's just swing your sword and then do nothing else for about 4 more seconds?
No I don't think you mean this at all. I'm willing to bet there's some lively abstraction going on at your table just like mine. But you can't say that one aspect of combat is abstract while the rest is letter of the law. D&D (and any other RPG I can think of) has always been about abstraction from top to bottom. In fact, before we had things like feats and powers, we had the DM. On one attack roll the DM might say, "you heft your mighty axe aloft and cleave through him from shoulder blade down to his navel." In another attack with the same exact mechanic the DM might have said "using the blunt end of your axe, you connect solidly with his head, caving in one full side of his skull. He drops to the ground, dead." And in yet another, "your axe slices cleanly between his ribs, and he drops with a thud. As you are about to engage your next foe, he seems to be trying to tell you something. You lean down to hear him whisper his last, dying words..."
It's the same mechanic, but in-game three very different things happened to achieve the same result.
XP is not an exception to the abstraction rule, it's yet another element. Just like hit points and stats and saving throws and every single number you write down on your character sheet that doesn't represent physical items like money or gear.
A grab mechanic does not and cannot encompass every possibility of what might happen when you try to take hold of something, and the DM is expected to improvise as necessary to keep the rules in line with in-game reality.
Now replace "grab" in this sentence with any other mechanic you can think of.
"An opportunity attack mechanic does not and cannot encompass every possibility of what might happen..."
"A bullrush mechanic does not and cannot encompass every possibility of what might happen..."
"A perception check mechanic does not and cannot encompass every possibility of what might happen..."
It's all abstraction based on a core idea. Grab doesn't have to be "grab," it just has to be sorta-kinda like a "grab."
Nevertheless, it does represent a specific action, that of physically seizing a foe. When I as a player announce, "I am grabbing the toad," it is understood that I mean both the grab mechanic (Strength attack versus Fortitude) and the physical act of grabbing hold. If the Strength attack hits, then my PC has physically seized the toad.
Sure. Player announces "I am grabbing," so you use the grab mechanic. Absolutely. But the success or failure outcome is not a pre-determined thing. That's where the abstraction comes in. On a fail, full-sized Vecna nearly breaks your wrist as he smacks away your futile attempt to grab him. On toad Vecna, toady leaps away from your grasp. Same mechanic, same outcome, different abstractions. On a success, full-sized Vecna is grabbed. You would do the same thing with toad Vecna. If you've grabbed toad Vecna, you can either say that he weighs the same as full-sized Vecna, or you can say that he's just so darned slippery that it's hard to keep hold of him, what with you wielding a weapon and wearing gauntlets and all...
I said "successful grab." I attacked with Strength. I hit toad-monster's Fort. The toad is grabbed. I now wish to dispose of it, permanently, before it turns back into a big nasty monster.
Apologies, I rail-roaded myself into one train of thought and forgot to address this.

See Azlith's response, his is better than anything I'd have come up with anyway.
