The use of the word "complexity" for this is particularly unhelpful, not only because people have wildly different ideas of what adds complexity, but because bulk of rules does not really determine complexity (there is a correlation, but it's not a perfect one). Consider Rolemaster, usually the whipping boy for rules complexity. Is it complex? Yes, actually; but not at all for the reasons given.
It's called complex because of its combat charts: it has one chart for every weapon, with a column for every armor type. Is this complex? No, it's remarkably simple. Roll one die, add one number, add one of a very small set of possible bonuses or minuses, look it up. You've, without having had to think about it, already and automatically accounted for factors like how different classes of armor handle different classes of weapon differently, things which in other game systems require complex, multi-step rules involving conditional logic and multiple cross-references. Rolemaster handles those things better than almost any game out there, and it does it without using any rules, or requiring you to do any work, to get it -- because all that intelligence is encoded in the data in those charts, precalculated and stored. In practice, Rolemaster's combat system is by far the simplest of any game that actually attempts to model even half as much as it does.
Where Rolemaster is complex is in character generation. Some of this is inexcusable: its use of classes and levels, its varying skill costs being determined by a chart when a formula would do just as easily, and how stats take three forms, only one of which is used 95% of the time. You can only chalk those up to the time when it was created, and the evolutionary way it was designed. But some of it is entirely justified, in how it adds expressive range to the character system (I'll talk more about this later).
Rules-light zealots tend to insist that rules only get in the way of roleplaying, but in my opinion, that just means they haven't learned how to use them properly. Used well, they exist to facilitate the game, and will do so far more than they interfere with immersion or momentum. Sometimes you want more rules and sometimes less, depending on the intent of the game, its expected duration, the kinds of things characters will need to be able to do, etc. but you generally always need some, because they serve a number of important purposes.
Player knowledge of world physics: Unless you never play anything but Psychosis, it's probable that your characters will know something about their own skills, what they can and can't reasonably expect to do, what is likely to happen when they do it, and how to achieve straightforward objectives. Can I expect to be able to jump over that gap? If I fight that orc, will I die of an infection even if I triumph? If my Foraging skill is 8, can I survive in the woods during the summer? How about during the winter? Rules help players and GMs ensure they're on the same page. Fewer (or less clear) rules makes it more likely that players will get caught thinking they could do something the GM thinks they can't, which causes all kinds of ugly problems. It also makes it more likely that players will fail to attempt something that should have worked. In both cases, it means players won't have their characters do things that their characters should have realized to do, and thus, breaks realism and immersion at the same time.
Granularity: If you're running a quick one-shot, it's no problem that characters tend to be shallow clichés, and results of their actions tend to be repetitive and unrealistic. It's okay that it's impossible to have the rules distinguish between two similar, but notably different, kinds of characters, because they'd both be described in game terms in the same way. As a game becomes longer, deeper, or more involved, or covers a broader range of possibilities (like a time travel or dimension hopping game), you need a higher degree of granularity. This shows up particularly in character generation (as mentioned above for Rolemaster), where you want characters to be able to be different from one another in ways that aren't just special effects and window dressing, but actually have an impact on game mechanics. You also want granularity in the system that determines the outcomes of actions, such as skill rolls and combat rolls, to add richness to the range of possible outcomes and to allow all that granularity in character generation to actually matter mechanically.
Consistency: Even the best GM can't be as consistent as the simplest written rule. Consistency can be a boondoggle if used inappropriately; a good GM knows when to deviate from it. But throwing out consistency entirely because of this is throwing out the baby with the bathwater. It is precisely because of the background of consistency that inconsistency is so impactful; get rid of consistency and you take away the impact of deviations from it.
Filling in the gaps: No matter how well practiced a GM you are, you will fall into ruts. There will be whole classes of things that should happen that you would never be inspired to include in your games unless something reminds you now and then. GMing is hard and takes up a lot of your concentration. You have so many things to think about at once! The more you can offload some of that work into something else (like rules), and rely on them to remind you of the things it's hard to remember yourself, the better a realistic spread of outcomes you can achieve, all while freeing more of your own attention for the things you can do best that rules can't do, like creative endeavors.
Of course, in all these cases, bad rules will do worse than no rules. A lot of the arguments made by rules-light zealots are predicated on the assumption that the rules you'd be using are bad ones. For instance, that they would take up more of the GM's attention than they would free; or that they would create as many unrealisms as realisms. To be sure there are bad rules sets out there, and some of them are the larger or more "complex" ones, others the more popular ones, in some cases both; but it doesn't have to be that way. There are good rules sets out there that are easy to learn, quick to run, inspirational to the GM, and achieve all of these needs -- though perhaps there's no single game that is all of these things at once!
Rules are the engine that helps the GM do the bits that can be easily handled by rules; they don't replace GMing, and GMing doesn't replace them, if you want the best results. Sometimes you want lighter ones and sometimes heavier ones, because sometimes you want to pull a lighter load quickly, and sometimes you want to pull a heavier load a longer distance. Let me conclude with a bit of silliness with some truth in it:
(note: plans are currently underway to put two more trailers on)
(someday, I hope to get a trailer...)
(note: gears are grinding because it's been overloaded with too many yummy pastries)
(yes, you can play a ninja... even in Bunnies & Burrows)
|Risus||same as FUDGE, but with all the safety gear stripped off for speed, then replaced with garish, fluorescent racing stripes|
(comes with the first eight pages of the skateboard repair manual, reprinted in medieval blackletter)