It doesn't matter whether you use free roleplay or any other methodology, you can't keep an RPG a game without also having the problem that certain subsets of players aren't able to play certain characters who are heavily defined by their mental or social attributes.
Let's imagine the easy case of wanting to play a Sherlock Holmes type character. You can give that player character any amount of investigation, spot hidden, and knowledge skills to gather all the clues you want, but if the player lacks the intelligence to put the clues together then they still won't achieve the effect of being a Sherlock Holmes type character. Rather, some other player at the table is likely solving the mystery revealed by the character's skill since the player lacks the personal skill to achieve it. Or perhaps you could have some sort of insight or intelligence check to determine if a character makes correct conclusions, but at that point the player has stopped playing their character in any real fashion. You the DM are now playing the character and the player is no longer involved in a game in which they are a participant, but merely observing you run a simulation on their behalf where they have no role beyond being the random number generator.
It is not possible to separate the mind of the player from the game universe. The mind of the player is a part of the game universe and as such the characters a player can play are limited by their mind. Try this with 5 year olds if you want a real proof of it. Attempts to "remedy" this situation don't result in player empowerment, but player disempowerment. The character acts according to the DM's narration or according to the dictates of the dice. If the character does act according to the player's violition, then you are left with problems like honorable characters can only be played by people who understand honor, funny characters can only be played by humorous players, and players can't play characters that are very much wiser or smarter than they are themselves. A little bit smarter or wiser you might could manage, but big gaps character skill alone can't overcome.