It takes a LOT of money to make some of these games. Millions of dollars, sometimes. A game like Saints Row (any of them in fact) can't feasibly be done by a few people together in a garage. You need a team and resources, making money for salaries and the like.
Think of a publisher as an investment company. A developer decides they want to make a game. Sometimes they have a good relationship with an existing publisher, but more often than not they have to find a publisher who will back the game. This will involve time, and a good ready presentation meaning some of the groundwork concepts have to be done. If they find a publisher, the publisher will agree to give them money to make the game and publish it, in turn for the profits. The deal cut varies.. sometimes it can be a percentage, but often it's just that they pay the developer a flat fee, and take anything extra as profit of their own. They also get some measure of control over the developer (not always, but typically) and can thus make sure the game fits what they think is profitable. After all, they're pouring a lot of money in, and if the game falls apart without being developed they're out the whole amount they put in with no return. That's also why publishers set deadlines.. the longer development runs, the more it costs.
It's the finding a publisher part that is often the hardest part for independent developers.. that and losing control. Kickstarter only goes so far, and very very few companies have the cash to be without a publisher (Valve for instance, but only because they managed to get Steam up and running, and that's all profit to them now as well as the sales of all their games). That there is the biggest reason that many developers (like say Volition) agree to be a house developer for a publisher, giving them the security of knowing they have a publisher for sure for whatever they make, at the loss of some autonomy. And, if it comes to some companies like EA.. ALL the autonomy.
Besides, the bills have to be paid even if they don't have a publisher... many companies have just gone bankrupt trying to find someone to publish their stuff as their reserves run dry, and often they sell out before that happens.
