Interesting discussion
In my RPG group, we always use miniatures in combat settings (which are plenty), to visualize where everyone is during the conflict. We experienced too often that the highly visual thinking members of the group (read: all of us) had wildly different interpretations of the proceedings. And this often resulted in discussions along these lines:
Player: 'I hit the left thug on the head with my cudgel'.
DM: '... But you are in the back giving fire support with your bow'.
Player: 'Yes I was, but last round I told you I moved forward'.
DM: 'Yeah, but not that far and there's a fire pit in the way too!'
Player: 'But those are all the way over to the right!'
DM: 'No; they are over here as well'.
And so on. You get the drift. Once we introduced miniatures and limited terrain pieces to our sessions though, this was instantly resolved. And I, often being the supplier of terrain and miniatures, had a reason to hunt for and paint miniatures for all the PC's and some important NPC's as well. Which is nice.
However; when not in combat, we solely do the Theatre of the Mind thing. Miniatures are just a great visual tool for us to keep everyone on the same page when things get chaotic. basically we play RPG's with wargame-light elements
In wargames though, things are wildly different (for us).
I am well aware of the origins of RPG games, but having been introduced to the hobby through games like Hero Quest and Space Crusade, gatewaying into Warhammer (40K), it was decades before I was introduced to other wargame systems, and by then I was so set in my ways, I had trouble 'getting' the RPG light aspects of some games.
An example that comes to mind is Infinity. In the rules there are abilities related to hacking for instance. And by edition 2, this became almost like a mini game in itself, with attack skills, defence skills and utility skills, all in the virtual world. I had no real problem visualizing this (hey; I read Neuromancer!), so this was to me just another weapon.
But then there are skills like Mimicry and Stealth. On the higher levels, these allow a miniature to either be invisible and not even present on the table (Stealth III; the owning player places the mini on the table before the game and takes a picture of its position (while the other player looks away), and this kind of works. But then there is mimicry, which allows a miniature to pose as one of the opponent.
And this requires a level of roleplay. Because the opposing player fully knows that the mini on the table right there isn't one of his. So his minis within LOS can test against the skill of the mimicking miniature to check if they can see through the disguise.
But just imagine: you're in combat. The enemy is right over there. And then a soldier in a uniform just like yours is moving around behind you. He's clearly one of ours, so stop getting distracted and shoot back at the bad guys. You know; over there.
Even though
the player knows that the skulking soldier isn't one of his, his troops on the table cannot possibly know or suspect (unless something untowards happens, obviously). Yet in every game where I have used this, the opponent started testing against the skill with every mini in the vicinity, regarless of whether it would be 'logical' for them to do so.
I've mentioned this a couple of times; put yourself in the boots of the mini on the ground and imagine whether or not they would be inclined/aware/suspicious enough to check against the imposter. It's an RPG element.
But Infinity, at its heart, is a competitive game (which is why I mostly turned away from it), and honestly RPG-ing such a situation might actually be detrimental to your results. So most, of not all, players will not stoop to that level and will make checks as much as they can, regardless of the 'logic'.
So this, to me, is a situation where RPG elements in a wargame do not work. And this is only enforced by the strict division between RPG and wargame I grew into back in the day.
Which is not to say that I am adverse to the idea though, and I've been well intrigued by smaller rules sets that offer RPG elements in their skirmish games. They've just never found traction in my group, but they still might; who knows