This Is MY City!
So much of the game is about making the player feel like they're empowered, and in that there's no shortage of praise. Many of the things that are tedious about open world games has been bypassed, making for a game where you can get nearly anywhere quickly (by calling in support, of course), and though I may bemoan the lack of variety to some of the side stuff, the challenges found in your phone alone can help extend play time with a buddy for almost as long as the main story.
Make no mistake, you should absolutely play Saints Row: The Third with a friend. The game was built from the ground up for it, and the experience is magnified many-fold over what you'd get if just playing things solo. It's perfectly serviceable if you, say, rent the game and thus can't use the included online pass (yes, this has one too), but you'd be cheating yourself out of an incredibly fun experience that very often you are making rather than the developers.
Whether that speaks to the tools Volition has offered or their lack of a cleanly-delivered means of doing it by way of the story is open for debate, but your motivation to experience what they've made most definitely is not. Play this game. Play it with a friend. Watch how quickly time flies. I can't think of a better indicator that something here is very, very special, even if the game proper isn't quite as refined as it could have been.