"FPP is bad for RPGs, because it seeks to put the player in the place of the character"
This is what an RPG is meant to be.
The hell it is. That nullifies the point of making a character; an identity with aspirations, aptitudes, and
limitations from a life growing up in the world of the game's setting. What you describe is costume.
RPG Characters are [effectively] the limitations by which the player can observe, solve, and influence the setting, based on what that character would do in the situation. If that character cannot accomplish a thing, then the player should never achieve it when playing them. They are not one in the same person. The player is probably a suburbanite, who has not experienced the life of the PC, and would likely act very differently in their place than they would. When the player runs the PC—a person (or creature) likely born in the game world, and accustomed to its other-worldly reality as their version of normal, they must ask themselves, how would that character react to the situations they find themselves in? What could their abilities, inhibitions, and willingness (if any) allow them to do?
(And ultimately... would these beliefs and behavior afford them success or failure?)
________
If the character were Indiana Jones, would he choose a path filled with snakes, if there was another way? Would he betray a colleague who trusted him at his word? Would he justify stealing from them? (...possibly)
If roleplaying the character Gandalf, would the player steal the One-Ring for his own use? Gandalf would not—Gandalf would not even willingly touch it; and knows it would twist him through his own kindness streak, and his willingness to do good. Choosing to steal the ring is out of character—even if the player wants it, they shouldn't get it when playing a PC who would not, or could not justify (or even manage) taking it.
If the character was the player's own creation, and they chose to create a streetwise thief who is alive because on the streets they stole daily to survive, including food from others in need of it—and thinks nothing of it... should that player not elect for them steal from others when given the chance?— even from friends, from allies; and even at risk of their permanent enmity, and —very inconvenient— lack of cooperation later? This is habit for them... it's what they do. A cleric PC might well choose to donate tithes at his church for himself and all of the other party members—with their own pay (if he is naive enough; ie. stat check); trusting that things will work out the best for them all, by his god's will...it being for their own good—sinners that they are.... and they'll probably hate him for it.
PC are not costumes with special abilities. It is not, "Cool!
I am a Wizard!"... it is, "This is Edwin, a Red Wizard, a talented psychotic, attracted to gaining power over others through spellcraft; a man who would think nothing of torturing puppies if it suited his wont. Clever, but over confidant. He takes unwise risks, believing he will succeed where others could not; and that tempers the player's choice in a situation. With Edwin you don't play the hero without an ulterior motive, and without considering the mark a gullible fool. Edwin would betray his own party members; even sell them as slaves.
RPGs use player character statistics and abilities to evaluate when to say 'No'; this is most important of all. It's what keeps it from becoming a "let's pretend" free for all where the Barmaids punch out trolls, and Halflings hitch rides on canon balls (because why not?); or "Who says I can't swim across it?", "Why do I have to get caught picking his pocket? I don't want to get caught!".