I'm going to start off this post by making some broad generalizations about people in the roleplaying game community.
1) We like telling collaborative stories with our friends.
2) We like playing boardgames with our friends.
3) We often want to do both 1) and 2) at the same time with the same people.
Fortunately, roleplaying game systems allow us to do just that. But not every story is equally well told by every RPG system. If your group is anything like ours you've run into what we've come to call the "limits of a system." As Jeremy mentions in his last post, it can be difficult to play Captain Malcolm Reynolds in a team of specialists using a game system like Pathfinder. The d20 System and its descendants all have a "roll-high" mechanic that determine outcomes based on whether or not a player can surpass a target number (Difficulty Class or DC). This encourages players to build specialized characters with a high single stat in order to bypass that DC so that they can feel like they're more successful.
The concept of a generalist character is limited by the fact that the d20 system, mechanically, heavily favors specialists builds. But my argument is that this is not a inherent flaw with the game system itself. I think that this is a problem that results from the dissonance created when a game system doesn't align with the type of story trying to be told. For example, if I want to tell a gritty, super lethal, cyberpunk intrigue set in a dystopian future I wouldn't use the Pathfinder or d20 Systems. HP and AC are great abstractions but don't perfectly capture the feeling of intense laser gun shoot outs or seat-of-the-pants hover car chases. I'd probably use Shadowrun or Paranoia (depending on how much hilarious backstabbing I wanted) because those game systems were designed with that setting and story structure in mind.
A roleplaying game system really shines when it is used to tell the stories that it was originally designed for. Dread is a great example. It's an incredibly effective storytelling system for how simple the rules are. 95% of the mechanics revolve around a Jenga tower. In order for your character to accomplish difficult tasks, your player pulls a block out of the tower. If the tower falls down, your character dies (or is otherwise removed from the game). You can also elect to intentionally knock down the tower which represents your character going out in a blaze of glory. That's pretty much it. Dread is a great system to tell a horror and suspense themed story because the mechanics support the slow building of tension that is so critical to the telling of a compelling suspense thriller. With each successful act there is an increasingly likelihood that the next act will result in both failure and lethality because the tower becomes more and more unstable. When the tower falls and someone dies, tension is released and the tower is rebuilt, only to come crashing down again at another dramatic peak.
As great as Dread is for horror, it's terrible for a pulpy, sword-and-sorcery type game. Dread assumes that most of the protagonists die by the end of the story. There's very little chance for epic greatness when your character is literally one action away from death at all times. If I want to tell a story about Conan the Barbarian, I want a system that assumes that the players win, forgives mistakes, and allows recovery from streaks of bad luck. I also don't want a system that has too many rules for elements outside the scope of the story I want to tell. I don't need to know how to handle acceleration and vector based turns or how much damage my character would take from orbital bombardment. What I do need is a system that allows me to tell a story where my character cuts the head off of a dragon and wears its skin for a cloak.
Now there are exceptions to this, of course. James Jacobs' Unspeakable Futures and F. Wesley Schneider's Mass Effect/Pathfinder mashup are a couple of examples of how the Pathfinder/d20 system can be adapted to genres beyond Sword and Sorcery. The key word there is adapt. Game rules will never perfectly capture what it's actually like to do the things we talk about in stories. It's all about verisimilitude. And ultimately it's a matter of group consensus that will determine which RPG system you end up using. Whatever is the most fun.