Roleplaying games tend to be arranged along an axis of complexity: rules-light games are very simple, rules-rich games are more complex. On its face, "simple" seems like a virtue, so why wouldn't we all use rules-light games? (This argument might seem absurd, but it's actually a widely made one.) Because that complexity buys you something. Or more accurately, three things.
Assisting the GM
A GM has to balance a lot of things. Keeping the story going in a satisfying direction, ensuring all the players are engaged and getting what they need, adjudicating conflicts, improvising when the players go in unanticipated directions, and playing all the NPCs, to name a few. Rules-light games also pile onto the GM a lot of additional work: deciding what various outcomes mean, inventing results for actions, etc.
A good, experienced GM can keep up with more of this stuff, but no matter how good a GM you are, there's always times when doing more of one thing means doing less of another. Having to spend more time thinking about what it means that the player just rolled that particular roll, means spending less time thinking about what the NPC's reaction should be, for instance.
And this tends to make us fall into ruts. Some kinds of reactions or events are closer to the forefront of a GM's thoughts, and will thus tend to happen disproportionately often. Others will happen too rarely, even though they might be fun or make sense (or both), just because the GM's mind doesn't run there as readily. Free up more of the GM's mental processing power and he's more likely to be able to think of unusual or uncharacteristic things to happen, as well as being able to make NPC reactions more fleshed out and less one-dimensional, pay more attention to keeping all the players engaged and having fun, etc.
While rules can occupy some of a GM's mental processing, they can also free up a lot of it by taking care of things for him. They can also allow the players to contribute to running things by handling their own arithmetic, table lookups, and to some extent, rules and action resolutions. In a rules-light game, usually the GM has to do all of that... in his head, off the cuff, in the moment.
It happens more often than you might realize, that your expectation of what your character can and can't do, or what the likelihoods are for various outcomes of some situation, don't match what the GM thinks. This means the decisions you're making for your character can turn out to be wrong through no fault of your own. You might try something with less chance of success than you'd expect, or fail to employ a tactic that would work if you had. Most of the time, this is a minor issue, easily overlooked. At its worst, you can get your character killed trying to jump a chasm that you think your skill should let you jump, but your GM doesn't.
Rules help to firm up a lot of these things because it's up to the rules whether your character can do this or that, and the way the dice work determine the probabilities in a way that the players can figure out (or just pick up from experience). It's never going to be a 100% calibration, of course, but there's a significant gap between a rules-light game where the outcome of a combat comes down to "the GM makes it up" based on the advice of a die roll, and a rules-rich game where specific wounds are determined by a specific numerical process.
Good rules tend towards being more "realistic" to the world setting and genre feel, by ensuring that all possible outcomes are possible, and come up with the right probability. Note that we're not talking about realism in the sense of accuracy to the real world: no one wants to play a swords-and-sorcery game where the dragon can't stand up because of the cube-square law, and can't breathe fire because of the second law of thermodynamics. But we do want one where the rules produce results that accurately simulate the way things work in that world, and that's why we say "verisimilitude" instead of "realism". Rules-light games can be only as accurate as the limited amount of the GM's mental processing available for ensuring verisimilitude can achieve, but as we make rules more complex, one of the main things we're aiming for is more verisimilitude with each extra rule or element.
So what is the cost of all these rules? They're real costs, and they're why for some types of games, rules-light is the right solution, and for some games, rules-rich is better.
Slowing The Action
More rules mean more time you have to spend looking things up, adding things up, figuring things out, and working with rules instead of with the world and the action. In the extreme case, a combat that represents a half-minute of frantic, action-packed gunplay and acrobatics can take a few hours to play. And that can mean by the end of the session you don't feel like you got very far, which can be dissatisfying. You don't come away with the breathless excitement you'd get from watching that same fight in a movie.
Intimidating Learning Curve
More complex rules tend to scare off new players. They see a big sheet full of numbers, and despair at the idea of being able to jump in, or have fun. They worry they're going to "do something wrong" and they figure they'll never quite figure out how to make a character that isn't crippled because they forgot something, or make the right choice in a combat. They might even feel like instead of playing a game they're learning something as dry and unexciting as chartered accountancy.
Disconnectedness From The Genre
Often the GM is trying to convey something of the emotion or atmosphere of a setting or genre. Running a horror game? You probably want your players to feel a little bit scared, a little frisson of chill up the spine. Your space opera might want to convey a sense of the vastness of the possibilities around us. Your game of mysticism wants to feel shrouded in mystery and symbolism. Your historical fiction should convey the sense of being in that period of history, or alternately, in the fiction from that period of history. Your modern suspense should make your players feel like they're the ones hanging from the chandelier dodging bullets as they try to get to the bomb before it goes off.
None of those things really dovetail well with asking your character to look something up on a long list of numbers, add it to three other numbers, then cross-reference the result on a table and record the result on another sheet of paper. (Unless you're playing a game set in a bureaucratic dystopia, maybe.) Rules tend to pull the player's focus away from the world you're trying to immerse them in, by pulling them to thinking about the rules themselves, the numbers, the dice, the hit points. It's like watching a movie and paying attention to trying to see the wires by which the hero is dangling, or guessing what CGI rendering engine they used, instead of being drawn into the story.
We usually assume that there is a simple cost/benefit process in play. Every new rule, or new element to a rule, that increases complexity, serves to increase the benefits and the costs. That's probably true in some sense, but it's an oversimplification. The real point is the cost/benefit ratio.
Some rule additions will add very little complexity, and thus, increase the costs very, very little. Some will add a lot. Some will provide very little benefit (or even, in the pathological case, no benefit), while some will provide a lot.
Game design is really all about finding the best ratios. Finding ways to add more of the benefits while paying less of the costs. The difference between a good rules-rich game and a bad one is not how many rules they have, or even how much verisimilitude they have, or any of the other benefits. The difference is how good a ratio they achieve between costs and benefits. It's easy to make a set of complex rules that accurately model weapon ranges or encumbrance; it's hard to make one that does so while still staying out of the way of the GM and the players.
The most important fact about game design that is typically overlooked or oversimplified is that there is a huge range of cost/benefit ratios available. Some of the rules employed in some rules-rich games cost a lot for what you get. They slow things down too much or pull us out of the world too much. But that doesn't mean some other approach, some other rule, couldn't do just as well (or better) while costing far less. What game designers need to be doing is finding techniques to maximize the ratio, more than worrying about where on the light/rich spectrum to fall.