Well, what I came up with for FF4 there should change things for the player if it's balanced correctly, but they're probably not going to know that.
If you took the ability to see the counters out of the counter system, it would look random and be completely pointless, because it really shouldn't change anything otherwise. The question at hand is: What should the player be able to know?
If you're playing an SRPG, then I see no reason why the player shouldn't be able to see whether they're going to be able to hit or not, as opposed to spanners being thrown into gears, given that they can't alter it without spending units' turns, and given that them knowing what the numbers are does nothing for them over half the time because that time belongs to the enemies, and given that the enemies have the same advantage. In a standard RPG on the other hand the player doesn't have much of a reason to need to know the numbers if that system was implemented, since a lot of them among other things don't let you control at which points your characters attack and such, and there are less units to pass the failure on to even if you do, not to mention missing/etc tending to be relatively less worthfull in them since among other things you don't have to worry about movement.
Similarly, why should they know when they're going to get into the next battle? Aside from games with encounter control/escape mechanisms, there's not going to be anything they can do about it. One argument could be that they'd know to heal themselves before entering the fight, but if they're that hard up they should have healed as soon as they left the last one, so it's on their head, not the lack of counter's head. And what I proposed is debatably better than just a random number, regardless of whether they know that or not.
Say we take attack variance in some game, and have it generated based mostly on increasing the closer the attacker's HP is to full, decreasing the closer the defender's HP is to full, and shifting in either direction due to what sort of weapon is being used compared to what sort of weapons the enemy doesn't like used against it, along with minor factors, then we have a debatably better variance system, and we allude to the player that they do more damage if they're healthier and such. And it still looks random because of the other factors, although it isn't. But it does change things because they can see that they're having an effect on it, assuming that this is a game with big numbers.
On reread, I guess this doesn't really mesh all that well with being a fixed number that you don't know anything about as you said. In that case we can allude to some of the factors in the encounter time situation as well. [EDIT] Beaten by Grefter anyway >_>