Y'know, while I admit that GTA V's characters are "inconsistent" for the reasons Yahtzee stated, I still somehow find the thing as compelling as all the other GTA games (maybe not as much as GTA IV and it's DLC episodes, but at least on par with Vice City and San Andreas).
It's certainly a lot better than most of the "spunkgargleweewee" crap where you play an emotionless soldier gunning down foreigners/alien monsters (with frankly little difference in characterization between the opposing forces) and committing "gritty" war crimes (such as the part where you shove a glass shard into a victims mouth, and punching it around the inside of his gums), and still told you're the good guy because you "fight for the good guys", or "all the guys you're shooting are EEEEEE-VILLLLL!!!", without giving legitimate motivations for why you're good, and why they're evil, apart from stock political talking points.
In a sense, I think Rockstar was deliberately trying to badly motivate the GTA V characters, as a sort of hipster-ish "ironic" jab at how other Triple-A games have main characters with even worse motivations - the difference being that the GTA V heroes, for how badly they're motivated, at least consistently admit they're badly motivated.
I personally think the actual plot is better digested as a "TV serial" kind of deal rather than a single, cohesive story. The episodic stories are brief, the main characters stay largely the same, but the situations they face and enemies they fight are radically different for each episode. The main draw isn't how the characters evolve over the series, and more on how they'll pull off this next job, and/or fight this new set of bad guys.
For example, the "Prologue" mission would have been the pilot episode for the GTA V TV Series, or perhaps the grand finale of a previous season of the GTA show. The first "episode" of the GTA V TV show is Franklin and Lamar doing repo jobs for Simeon. The second episode would be around when Franklin tries to repo Jimmy's car, and is ordered at gunpoint by Michael to smash up Simeon's dealership. The next few episodes would revolve around Franklin doing favors for Michael, hoping he could pass on some expertise to him, before culminating with when he helps Michael tear down the house of a guy sleeping with Michael's wife - and both of them end up owing $2.5 million to a ruthless drug cartel lord. The final episode of this "arc" would have been planning and executing the Jewelry Store Job, and paying off the drug cartel lord... only to "reveal" Michael's old partner Trevor is still alive in Blaine County, and now knows that Michael is back in the game.
Then we have the episodes of Trevor wrapping up his business in Blaine County before going to Los Santos, then the arc where Trevor forces Michael to work with him as repayment for the job gone wrong in the Prologue, and then the arc where the FIB men that gave Michael witness protection see he's getting out of line, and force him to do dirty work for them 'lest they expose him to the world at large, and so on and so on until the last mission, which is the "Grand Finale" of the whole game/TV season.
True, TV has proven there are shows that can have consistent and conclusive character arcs over the course of the show, and there are shows that suffer from not having consistent motivations for their characters, but GTA V is kind of in that sweet spot of having characters that are interesting enough to bounce all kinds of crazy scenarios off of for a game about as long as a TV show season.