In some rare cases, rules tweaks can bring borderline cases back to participation. For example, streamlining combat or task systems can take a game that has an issue and make it more playable.
But in general, problems with individuals tend to be deeper than rules; setting is often far more important to individual players than the rules.
Going through your examples:
- Someone is not really interested in the game, and reads and ignores play until they have to roll.
Rules tweaks to the current game probably won't help this one. A change of game, character or setting might, but don't count on it. Flat out ask them why they play; pay attention. If they are not there for the game, then perhaps it's time for them to find something else to do.
- The GM favors certain players over others
Again, rules tweaks won't help, but certain mechanics are capable of reducing it. Problem is getting the GM to play those games. Burning Empires has a scene budget mechanic that gives every player equal numbers of scenes, and the players focus the scenes themselves, so the GM just sets action difficulties.
- Two players have an out-of-game disagreement and it is showing up in the game.
A set of table rules might affect this, but it's beyond the scope of the game itself. Simply put, humans don't isolate stuff well, and it is bound to leak through, but it's also not something where the game itself will help.
Switching to a PVP system (such as Houses of the Blooded) will actually tend to exacerbate such behaviors.
Talking to them about it might help, however, and will at least have the potential to get it moving towards resolution. It could also result in a nasty blowup, argument, and storm out.
- Players make last-minute cancellations or can't prioritize a regular game time.
An in-game penalty for no-call or late-call no-show can reduce that, but it also can be a stressor that breaks a group.
Players are real people with real life. If someone's in an on-call job, accepting them into the group includes accepting that they may be called out just before or even during session. If someone's blowing you off for a good book, odds are the game isn't why they're playing.
Some players just never get into it as a hobby, seeing it merely as a way of passing some time. Just give them characters easily written in and out of the ongoing story... A deranged vapire with MPD comes to mind from one friend's Werewolf campaign...
- The GM can't tolerate deviations from the story.
Again, no rules tweak will solve this. This is simply someone who probably shouldn't be GMing. The story should emerge from play, not follow some arbitrary script the GM has thought up.
It's fine to have boundaries, especially if everyone has agreed it's time to use a module or specific adventure. But in more sandbox-style campaigns, no, this is bad GMing. And I'm not generally one to claim "Badwrongfun must stop!" But in this case, it's obvious that, for you, it's not fun, and "badwrongboring" and "badwrongannoying" really make it a pain.
Solution? Try a different GM.