No, but insightful characters should.
Does a strong player automatically break free of grapples?
...a player with strong Willpower succeed on Will saves more often?
You example is flawed.
You are measuring my willpower against the game modifier to a Will Save. The answer is inherently No because my willpower is not represented in the game.
That's like asking if a dextrous player should have a higher AC? No.
This is then akin to Should a charismatic player get more henchmen? No. Because the tables say exactly how many henchmen you get, by your charisma score.
What the rules do not cover is how many good ideas you are allowed per session. it does not cover how you may phrase your statements to NPCs. It does not cover what the player may guess or deduce from the information presented to them.
there are literally no rules declaring how your PC must act if his INT, CHA or WIS is 6.
There are no rules preventing you from coming up with a good idea. Or to prevent you from executing on that good idea.
If I am so insightful that in the first encounter of the night with the NPC who is giving us our quest that I figure out he's really the bad guy and this is a screwya mission so I kill him, then so be it.
As a GM, I don't think you have any right to stop me (outside the bounds of the NPC defending himself, other NPCs coming to his aid because a PC just went postal, etc).
You tried to screw me and my intuition correctly deduced it and bypassed all of your adventure.
In the game world, my PC may be obligated to follow social norms and have a burden of proof (like how do I get out of what appears to be a spontaneous homicide). For the player, I get to act on whatever idea comes to mind, barring violation of the player/PC information barrier.
If I learn something the PC could not know (like seeing a note passed by another PC to the GM that it turns out the NPC is a bad guy). That's different than me listening to the NPC's proposal and just realizing that this dude is totally setting us up.
at that point, what the player thinks is equal to what the PC thinks.
For [MENTION=762]Mort[/MENTION] case of arguing the same point and seeing it disagreed with:
If a bunch of people disagree with you, you gotta consider that they have a point.
The physical stats measure VERY concret things in the game world. They are OBJECTIVE units of measure. 18 STR clearly grants a +4 to hit and enables carrying a set encumbrance load.
How wise is 10 WIS? Obviously it doesn't grant any extra spells or bonus to a willpower save. Does it prevent me from making rash choices? Does it force me to make rash choices over prudent ones?
The rules do not cover that.