I don't see any problem with your house rule, but I'm not sure it's really applicable. Part of the problem is terminology--there's a difference between a round and an action or "turn."
In any round, people take their action according to initiative. If my mage character is fighting an orc, and I win initiative, I get to act first in the round: my action is my turn. Suppose on Round 1 of the combat, I try to hit him with my dagger and miss. He then takes his turn and tries to hit me with his weapon--that's his turn.
For Round 2, I decide combat just isn't my style and cast Command, telling the orc "Freeze!" He hasn't had his turn yet--so if he fails his Wisdom save, when his initiative comes up, that is "on his next turn." He loses his action that round. So the rule has the effect that you want, at least as far as that goes.
I'm not finding anything in RAW one way or another, but it seems to me that any action that the orc could take, including fleeing combat, would be covered by that Command as long as he failed the Wisdom save.
In addition, to my eyes the Opportunity aspect is a gap in RAW.
The Command spell has other examples can effectively put the target "out of combat": for instance, "Drop" will make him drop his weapon, "Grovel" will make him fall on the floor. But as written, the target would be able to take a reaction that round, and then freeze, drop, or grovel the next round.
To my mind, that makes no sense, so I agree with you that the rule change is a good one. If I were GM, I would write that rule change so that if the target fails their Wisdom save, they cannot take a reaction until their next turn after they have performed the Commanded action.
This does not unbalance the game, so long as you remember that enemy casters can also use this spell, and use it to the party's disadvantage.
I use the following house rule:
All monsters act on the same initiative. Player initiative determines who goes before the monsters on the first round, but after the monsters act the players can generally go in any order (usually in seating order, clock-wise around the table) because they will all go before the monsters' next turn anyway.
Notes:
- Since monsters of the same type normally go on the same init anyway, this just takes it one step further.
- For the monsters' group initiative: I use a 'passive check' (10 + average dex bonus) for extra-balance. (if desired, average dex bonus can be proportionally derived so that a high-CR monster isn't unduly altered by a single low-CR minion).
- You can instead roll the initiative, but it can be less balanced (i.e. easier or harder) when all the monsters share the same roll. Also, a passive check allows for speedier starts, and the players' rolls matter more.
- In practice I have the players roll init and say "Raise your hand if you beat init 12" (for example), then allow those that raise their hand to go initially (usually in seating order).
- Yes, this could allow a lucky player to go twice before an unlucky one went once, but they're competing against the monsters (not each other). Plus, this method actually doubled the rate of play, so the end result was more playing for everyone.
- The reason it doubled the rate of play is because it also allowed me to easily skip past anyone that wasn't ready (coming back to them once they were ready).
- The phrase "You'll all get to go before the monsters' next turn anyway, so I'm not too worried about the order" seems to garner buy-in even from traditional players.
- I've used this house rule for over a decade. It has done well through many discussions on the old WotC boards, dozens of conventions, and dozens of campaigns with different groups.
Best Answer
Why would you Shove without a follow-up?
Knocking someone down is not really a good strategy in any fight (real or imagined) if you don't have a follow-up. When was the last time you saw a UFC/MMA fighter push someone to the ground and then just let them get up? When somebody in a gang does a shove, they're doing so to let their friends jump on the fallen.
Once you knock someone down, your next step is really to Grapple them or attack them while they are on the ground. A Grappled creature's movement is reduced to zero, so you can effectively prevent them from getting up (like the gang above)
In fact, the Monk actually do this Shove and Attack starting at level one with their Martial Arts skill. So you knock somebody down (Attack Action), kick them in the head (Bonus Action) and even step away if you want (Move Action, their AoO at Disadvantage). If you move away, they typically can't attack you on the following round because they have to waste their movement standing up.
Note that at 5th level a Monk (or other PC with Extra Attack) could do both a Shove and Grapple as part of the Attack Action to effectively pin their opponent. Escaping the Grapple requires an action and standing requires half movement, so pulling this off pretty much wrecks the target's turn.
This is clearly a gang-up tactic, but that's expected.
Is Initiative the Problem?
Consider that the problem here may actually be the initiative order itself.
You point out the problem of effectively "metagaming" the timing of the action, but also the problem that it will basically never allows you to benefit.
DMG (P.270-1) presents an alternate initiative system titled Speed Factor.
This is followed by some modifiers for speed and action type. The action order in each round is random (weighted). This means that knocking someone prone will always have at least a chance of being useful. And there's no "house-ruling" required as this is straight from the book.
If you're really worried about the metagaming aspect of Shoving/Grappling etc. this might help as well. I've used this "initiative per round" and it does kind of solves the problem of gaming the initiative order, both for things like Shoving and for things like Healing. However, it introduces other problems like wasted Actions. So it may be a little much just to solve the Shoving problem.