If a character describes doing something I often won't call for a roll at all, I'll ad hoc adjudicate it. If there is something to figure out I often give no roll at all. In combat there is a ton of rolling and hard mechanics. If I want to run an abstract skill challenge type of thing I'll call for rolls of some kind and often end up ad hoccing DCs and results.
I could care less how a player plays his alignment. If alignment has a mechanical effect like in unholy blight I'll look at the character sheet, otherwise I could generally care less how he matches what is on his sheet. Most everybody has their own views of what the different alignments are about and how their actions map to different alignments. I have no interest in bending others to my views on alignment as a DM.
As I said (much earlier in the thread from what I recall), this is great if stated up front, but can be a problem if it's not.
2 people sit in front of you, one who knows the way you run and one who does not.
The one who knows the way you run is likely going to give short shrift to INT and CHA unless his concept mechanically demands it because he knows it won't matter much (from what you just stated in your post).
The other one, wanting to play an intelligent or charismatic character will sacrifice to get one of those stats up and maybe sacrifice valuable skill points - only to realize at the table that it was a waste to do so.
Mental stats and social skills and alignment are not the primary consideration in roleplaying a player character. These are generally vague categories with a few hard mechanics. I'd much rather a player play his character the way he wants to than try to emulate numbers or boxes checked on a sheet. When the hard mechanics come up I'm fine using them but using ability scores and skill ranks as defining how to roleplay serves only to limit appropriate roleplay to no real benefit IMO. I'd much rather the player focus on how he conceives of his character and interacting in ways that are fun for him and the group.
I have a problem here. If you stat you're character one way, but play him in a way totally different - are you roleplaying the character? If you give your character an 8 INT but play him as god's gift to problem solving -is this really roleplaying the character?
If a player likes to roleplay being a smart and charismatic hero in D&D I don't want him to be limited to classes that mechanically use int and/or charisma to make a mechanically effective character. If he wants to roleplay as a wise and charismatic good guy like Hercules from the old Legendary Journeys show that is a fine roleplay concept regardless of what class he picks or what level he is.
I see no benefit in voluntarily limiting engaging roleplay to high charisma characters. I want as much of that as I can get across the board from every player regardless of what class they play. If someone is playing a foolish or mentally slow or shy character I want it to be because they think it will be fun to portray such a character, not because they like martial characters, dislike vancian magic, and chose to make a high strength and con fighter in a point buy 3e/PF game.
Part of the fun of roleplaying (for me, anyway) is fit into the selected(or assigned) role. If that's not partially defined by my mental stats, why even have them?
Notice btw, I'm not even saying the player is necessarily constrained. The player can play the character how he likes, but the stats determined how he is received by the world, the NPCs etc.
For example, if a player playing his CHA 8 character is playing the smooth negotiator I'm not going to be nearly as liberal with his words and reactions to them as if he had a CHA of 18 or even 12.
Or if an INT 8 character is trying to play god's gift to problem solving I'm not going to be as forgiving of mistakes as if he had an int of 18 or again 12.
Also, There are other solutions, rather than ignoring the stat for the "character you want to play":
Allow players to assign their stats (not point buy, literally assign). This way players get the stats they want and the characters they want to play. While this may seem subject to abuse, IME players are much more conservative than you would think, and yet get the character they want.
If that's too drastic - have a bonus skill or two. Someone wants to be good at diplomacy? they're trained in the skill for essentially free - etc.