So if I play up a character's flaws well, that should be "rewarded" -- that is, punished -- by the scene, but if I mostly ignore my character's flaws and play them tepidly if at all so there's no story effect I should be effectively rewarded by not being punished? Sounds like a recipe for Mary Sues who never RP anything except that which will advance the plot, as opposed to well rounded and interesting characters with fears and flaws.
White Wolf had RP as an important mechanic back in the 90s, in Vampire where PCs needed to act to either their inner belief or outer presentation to recharge Willpower, and important and oft-spent resource. Pendragon predated that in the mid 80s with mechanical tie-ins to RP. It was picked up, first by smaller games like Lady Blackbird or Don't Rest Your Head, but since has become common.
The state of the industry has moved quite a bit to mechanically supporting RP. Games like Fate allow you to play those downbeats for meta-currency (like Inspiration) that you use to make yourself cooler (like Inspiration) at later points. Cortex Prime, a vast selection of the PbtA games, all have this.
Frankly, to be called a Role-Playing Game, you need to have mechanical game effects to be connected to role play. It's literally in the name of the hobby. D&D is very late to the table with that sort of support, and those who mostly/exclusively play D&D and D&D-like games don't get how backwards that is. It's like if you've never driven a car with anti-lock breaks in today's day an age, and then bemoaning that it's not needed.