That's great, but they lack the versatility of Bobby Hill yelling "That's my purse".
Improvise Action is a thing and is in the core rules. The player dictates the action and the intended effect, the DM adjudicates whatever skill check, if any, is necessary.
Is it a robust and well integrated part of the game, no, but there again not a lot is.
But it is there. And you may come back with this being a mother may I issue, but the thing about that is is that we're now approaching an expectations problem.
For one, DMs shouldn't be arguing with players over something as simple as kicking a dude in the giblets.
And for two, 5e as designed emphasizes rulings over rules, and it does give you the tools for that. They may be disorganized, but they exist, and they demonstrate that 5E isn't a game thats intended to be overthought to death.
Like the aforementioned Bobby Hill special. That isn't a complicated action, and it doesn't take an argument to understand getting kicked like that will Stun a person momentarily, and given you're probably aiming that kick at a fantasy warrior or monster of some type, it probably won't take them out of the fight for long. If the improvised attack hits their AC, Roll 1d4 to determine how many turns the Stun applies.
Easy. Zero reason to overthink it and both players and DMs should know better than to start arguing over this.