But, perhaps surprisingly given the sandbox on offer, it's when you're following the story of the Saints and their efforts to take over Steelport, that the game is at its best.
Missions place you in increasingly unpredictable situations. It starts out fairly low-key with a raid on a military base to steal weapons for the gang, but it finishes with an explosive finale involving tanks, jets and city-levelling explosions. In between, there's a zombie outbreak, a trip inside a Tron-like computer world and... well, we won't spoil the surprise. But it gets wilder and more varied.
There's also an element of choice to the decisions you make. Certain missions see you choosing between two options that will affect the story, sometimes in quite dramatic ways. One example - and we'll keep it vague to avoid spoilers - gives you the option of destroying a skyscraper, or saving it for yourself. Impressively, decisions are tough, and never black and white: there'll always be a negative for every positive. It gives the story some flavour, and adds an incentive to replay the game.
Ultimately, though, even the missions have a problem: they're fun initially, but then the joke wears thin. They almost always devolve into tiresome bouts of endless, boring shooting.
Volition are full of ideas, but few that last beyond that initial burst of creativity. A few are an absolute triumph - usually the ones involving large environments and skipping between vehicles - but most are tediously linear, and no more interesting than a very basic corridor shooter.
And, before we get back to the good stuff, there's more sadness.
In most open world games, there are endless 'filler' side-missions blinking on the map that you try your best to ignore, and usually can. Saints Row, instead, makes you do them.
These 'activities' range from mildly amusing, to utterly mind-numbing, and you have to do all of them at least once, and sometimes twice, to advance the story. In one of the best, there's a tiger in your car and you have to keep your speed up to stop it mauling you. But most of the others are infuriating escort missions and wearisome on-rails shooting sections.
Similar problems eventually hinder the sandbox too. The play area is full of things to do and mayhem to cause. Some elements are more entertaining, and worthwhile, than others, but there are a lot of distractions. One of the biggest is being able to build your empire. Stores and buildings can be purchased, increasing your hourly income (that's game hours, not real ones).
By becoming a property mogul, you can have thousands of dollars spilling into your account; perfect for buying weapons and upgrades. It's optional, but very useful. You can even add additional floors to some buildings, turning them into skyscrapers and allowing you to reshape the city.
Character upgrades include being able to recruit more gang members, take more damage, and carry more ammunition. Weapon upgrades give you more power and accuracy, and other effects like armour-piercing bullets for your SMG: useful when the anti-gang 'STAG' military unit show up in Steelport.
Other distractions are more instant. Jump on the roof of a car and you'll start a 'car surfing' mini-game, seeing how long you can hang on without falling off. The insurance fraud mini-game, an old Saints Row favourite, sees you throwing your floppy, ragdoll body into oncoming traffic to try and injure yourself as horrifically as possible.
Then there's Professor Genki's Super Ethical Reality Climax, a game show that sees you battling through an arena killing guys in animal suits for money.
But then the problems begin. Because the gameplay at the core of the side content is all so rudimentary, the imagination of the developers seems wasted. It's as if Saints Row has more ambition than the technology can handle. The engine is vastly improved over previous games, but it's still unreliable and glitchy.