After seeing your comment on a recent episode, I think I might have a perspective for you.
Power gamers with a history of D&D, huh? And I see you give some ideas about “roleplaying mechanics” in the form of Champions Disadvantages and Fate Aspects. I have a two-pronged discussion about this.
Which iteration of D&D do you play? 5e? What would happen if you went back to Original or 1e? In those games the power bloat to superhero status is not present, and—most importantly—there are no Skills (outside of the Thief’s specific abilities—okay, some Ranger, too). Have you read Matt Finch’s Quick Primer for Old School Gaming? His thesis essentially is that the lack of mechanics promotes roleplaying. In other words, if there are no rules to accommodate rolling for task resolution, the players have no choice but to describe—or roleplay—how they do just about anything.
But, of course, you are asking for roleplaying mechanics. Champions Disadvantages thrusts complications upon the PCs. Cypher allows Intrusions. I’m not familiar with Fate, but it seems that some systems allow incentives for roleplaying. This seems to be the most prevalent mechanic for encouraging roleplaying: incentivizing roleplaying. Currently I’m running Modiphius’s 2d20 Conan. That gives the GM a resource called Doom with which to complicate situations for the PCs, and each PC has a Trait that, if they lean into it (in terms of roleplaying), can award them a resource called Fortune points. Still, this leaves a lot of indeterminacy and value judgments for the GM; it could be a problem for power gamers who, say, invoke their Traits fairly lamely and then demand rewards.
My own practice is this: avoid rolling as long as possible. Let’s consider those games (including Conan 2d20) that have social skills. For the most part, when a situation first comes up, ignore those Skills. Roleplay the encounter until one side—the GM or the player—is tapped out. Then make an evaluation. In my 2d20 game I’ve roleplayed encounters so successfully that no roll is required*. Is there some question of success? In this case I use an evaluation of the quality of the roleplaying (would the player have convinced me, were I the NPC? did the player choose to resolve the task in a surprising way?) to assign a difficulty to the task. In this way “poor” roleplayers still have their Skills to fall back upon, but they have to get there first. Chances are your players might be too eager to roll. I would say to them, “No, we’re not there yet. I don’t know what the Difficulty is. What do you say next?” Or, “How do you do it? This is important.” In other words, the players still have their carefully “built” stats, but they have to roleplay for an evaluation of how well—or even how—they use them.
*2d20 has a very interesting feature in that a player can still use a Skill for a task with “0” Difficulty. The incentive or “purpose” for this choice is the chance of generating a resource called Momentum. With every Skill roll, though, there is a corresponding chance that the player will generate a Complication. This is the risk/reward dynamic of 2d20 and many other games.