I'm aware of how it works. But that's not why they're established as likable characters. The game spends a ~lot~ more time ensuring we understand why they're likable people. The script spends a lot of time helping us understand their wants and needs, puts them in predicament after predicament where they have to do things we would find admirable. It spends a ~lot~ of time ensuring we get their camaraderie.
Saving Jimmy is literally nothing in the game's plot and it doesn't do what you say.
This is how Save the Cat works. It promises a formula, pretends that this shit is easy to understand, but it's like a horoscope. You find one moment that seems to do the thing it says it's doing, and you go "ah, see, it works," but there's a world of difference between a game where a character does one likable thing and GTAV, which spends literally ~hours~ trying to make us empathize with its characters and their plight. Rockstar also loves to make us hate the villains more than the shitty people the protagonists are, so it gets us on their side by making bad shit happen to them that we wouldn't want to happen to us.
If you fail to have a "save the cat" moment early in the game, it doesn't matter how many hours you spend trying to make the character likeable. It won't work. You will never win audiences back. Games and films that fail to do this suffer, so screenwriters insert these moments of small heroism, selflessness, and so on to impress upon the audience that even if this character later murders a puppy, the initial impression sticks. The director of the original Kane & Lynch admitted this. That although K&L have moments of humanity and selflessness, these moments were too late in the game. They had to appear early in the game if they were going to have any effect. (Of course K&L2 abandoned all efforts to make the pair likeable in favor of pure chaos and hate, which was quite effective in its own way but the game was NOT appreciated for its dedication to art and storytelling.)
You might not like Save the Cat, and you're not alone in that, but it is a screenwriting trick that is widely adopted across film and games. There's a reason these cynical "Has a heart of gold" moments are calculatedly inserted into stories fairly early in the arc. Some might call that plain good storytelling. But it appears so often because Blake Snyder was so liked in the Hollywood screenwriting community and his book was so popular. Also because games want to be movies.
Saving Jimmy is the first moment in GTA V when the characters are extremely temporarily portrayed as genuine heroes. Before this, Franklin was stealing cars. Before this, Michael was whining to his therapist. A washed up nostalgia-driven man with no direction. Before these characters launch into a life of crime, we are given a brief glimpse of them at their best. Risking life and limb for a dumb kid. It's not important to the plot. It's important to character impressions.
Trevor doesn't have a Save the Cat moment, in part because he's introduced midway through the game. Instead, he is forcibly given a trait to gloss over some of his horrific aspects. His almost obsessive respect for women. We haven't had control of Trevor for too long before we discover that he really, really, really respects women. And one could handwave that as a joke, but it's more than that. It's a single character trait inserted an absolutely awful character that makes them charming.
