Spoilers for GTAIII through IV ahead.
I think it's worthwhile to note that they tried something quite different tonally with GTAIV. In fact, since GTAIII you can see that the tone of the story and the atmosphere in each of Rockstar's cities is remarkably different. Liberty City in GTAIII and IV not only have drab weather and grey buildings but also deal with comparatively silent characters with rather vague aims of starting new lives and getting vengeance. If we analyze their storylines GTAIII comes off as relatively rather directionless, serving more as basic means to get the main character to explore the city and meet the various factions and do jobs. After all, it appears you only get a chance for revenge on the treacherous girlfriend because she decides to pop her head out at the end of the game [side note- was it just me or was that last mission really hard? I ended up relying on the bulletproof jeep to beat it].
Anyway, technically speaking, having a silent protagonist makes it easier to "feel" like you are in the game but it didn't work too well when it came to making interesting cutscenes or building a sense of connection between the characters. Hell, the most memorable thing your character chooses to do [outside of your agency] is the startling act of apparently shooting Maria after the end credits. Jarring as it was [and potentially disturbing to those 'playing themselves' as the protagonist] it actually kinda made ludonarrative sense given that to the guy can't help coming off as a sociopath silently listening and completing orders [if i remember rightly he'd just sway shoulders back and forth], with no apparent connection to his actions or their consequences. Personally I figured the guy had deep-rooted issues with his parents who never loved him enough to teach him how to swim.
Vice City and San Andreas not only benefitted from far more colourful settings but nostalgic timeframes that lend themselves far easier to Rockstar's brand of social satire coming across as less cynical. Making fun of things that went on in the 80 and 90s is less depressing than commentary on more contemporary situations. Thus Vice City's Scarface / Goodfellas storyline and Miami Vice cartoonish colour scheme justify or at least dilute how distasteful the violence would seem. Likewise, CJ's 'reclaim the streets' tale interspersed with outlandish NPCs and self-referential callbacks again dampened the ugliness some people might have found in the violence.
In contrast, like others I found GTAIV to be a slight misstep though I can understand how it was made. Rockstar tried to create a far more gritty, and indeed satirically scathing, experience that hit much harder at the still lingering idea of 'The American Dream' and how in reality the truth falls so far short of everything it promises. On top of that, the storyline quite ironically hammers home that no matter how noble one's intentions might be violence only begets more violence and that a life of crime might pay but it costs too.
But yeah, let's wrap this up- it's debatable how much Rockstar's choice in their method of storytelling affects how fun the game is, but if we're talking about games being art [and it's apparent people are] it would help if we could start distinguishing how different games are offering us varied relationships with our protagonists. Sure, most may tend to either aim to give us as free rein as possible or put us in shoes that make us feel like empowered heroes but increasingly we're being given opportunities to question who we are playing as... and this is a good thing that should be encouraged [even if it won't always work].
TLDR: So, GTA V has us playing as Breaking Bad / Heat characters? Doesn't that create less dissonance than one that suggests he wants to 'be a good guy' before shooting / blowing up half a city because someone else did something bad [or told them to]?