In my view, it's up to the player to play however he or she wants, allowing the ability scores to influence decisions for the character or not. I don't concern myself with such things when I DM, nor do I see any compelling reason to start. I adjudicate fictional actions taken. I don't sit in judgment of whether an idea the player articulates is something the character could come up with. If the player is playing to established characterization, I have Inspiration as a reward.
I reward going
beyond what is required in all aspects of the game. Proper role-play is expected. That's the reason we make characters that are more than just lumps of stats to begin with. Even Muscle John over there with an 18 Str, an 18 Con and an 8 in every other stat has personality and wants and needs and loves and hates. I expect his player to play his character accordingly. If the player has Muscle John do something incredible that goes above and beyond the call of normal every-day role-playing expectations, that's what earns rewards. XP rewards you enough for doing what you
need to do in order to win. Inspiration, Boons and other goodies are rewards for going beyond that.
So, in your game, the smart play for me as a player is to simply act on good plans and tactics I've thought up rather than voice them beforehand so as to avoid you asking for a roll to see if the character could come up with such good plans or tactics in the first place, based upon your assessment of my character's Intelligence score. I could live with that (because I'd rather do stuff than talk about doing stuff), but you should be aware that this is what you're encouraging.
Sure it is, and I wouldn't find it unreasonable for Muscle John to think that acting on his own might be better than potentially failing to properly communicate his plan to the party; I see that as good role-play. Muscle John doesn't understand strategy and tactics, so when everyone starts strategizing, he gets antsy and starts looking for something to punch. That's great IMO. But there is room for metagaming at my table. Bill and Bob are welcome to talk, as players, even if Bob's character is a moron, Bill's isn't, so Bill presents Bob's plan. That's fine and dandy with me. I give players room to do that. They're welcome to take a "time out" to discuss strategy outside of their characters. It is a
group game. Players
and characters should be working together to achieve their individual and mutual goals.
But Muscle John might also find out that acting on his own presents extreme danger to both himself and his friends. So
attempting to communicate a plan or taking a "time out" to strategize is worth the added effort, not to mention can also result in some exemplary role-play while Muscle John attempts to babble his way through strategy but his friends, being the understanding sort, make their own checks into figuring out what he's trying to tell them and we experience some great character development and have moment the table will remember!
What Intelligence score does a character need to have to come up with a good battle plan?
It really depends on what the player wants to do. Is his plan "Lets attack them while they sleep!" I think that's a plan just about anyone could think up. Is his plan, lets send two men over to that ledge where they'll do this and that and send another guy over there where they'll do some other things, etc..." heck, even the 18 Int Wizard might have to make a check if the plan is complicated enough, shoot it might even be too complex for the rest of the party to properly execute!
A "good" battle plan, something middle-of-the-road-ish? I'd say an 8 at a minimum. I don't think that's unreasonable.