It gives you a clearer picture of what the character does
When I first started playing my most frequently reoccurring character, it was in World of Warcraft, and she was a Warlock. She didn't get a lot of play there due to my not particularly enjoying Warlocks. The next time I made her a melee class, but she still wound up dabbling heavily in magic because she had the background for it and it made logical sense to give her a bit more breadth of ability.
Over time, the most important aspects of her abilities have become more and more pronounced. In Guild Wars 2, she was a Thief because she needed to be using firearms and she needed to be able to dual wield. That also made it clear to me that trickery is far more important for her as a character than straight offense. In Final Fantasy XIV she dabbled in magic, but it became clear that she was more interested in theory and utility than directed magic in battle. As I've played her more and more and made the choices that feel right for her, I've grown to have a clearer picture of what sort of abilities she should have.
At this point, if (when) I make another version of her in WildStar, odds are good she'll be a Stalker, which is a far cry from the caster I started off with but still has its roots in mechanical iteration.
It makes your limitations clearer
Guild Wars 2 bears a closer examination because mechanically, this character couldn't use magic in that game. That didn't mean that she was actually incapable of using magic; she could summon small flames, could undo magical wards and locks, and had mastered a number of useful traveling spells. She just wasn't capable of casting any spells that could be useful in a combat situation because that wasn't her focus.
In The Secret World, she had no such limitation. But even though she was mechanically using magical abilities, in character terms, her magical skills were limited to utility. That's one of the limitations of her character.
No one can do everything well, but mechanics lead us to giving everyone a certain amount of implied competence. When you've played the same character more than once, though, you can easily give that character limits that make reasonable sense. There's no reason I couldn't have had her be more skilled in magic in The Secret World except that she usually isn't talented with magical combat. The limitation from some games has carried over elsewhere.
You can do the same thing just as easily with new characters. Your mage can cast fireball spells, but maybe that's all he can do. Maybe his abilities are limited to combat spells because those are the easiest to master. Just because the game terms you a master of the arcane doesn't mean you can't work within that framework, especially when all the mechanics say is that you can cast spells X, Y, and Z.
It restricts you
The biggest benefit to mechanical restrictions are exactly what they say on the tin. You can't just do whatever you want with your character; you have limits. That means you have to be just a little more creative in your character's abilities.
In The Secret World, I had the problem of making a character with more skills than characters can actually possess in the game's terminology. You can have two weapons equipped at once, but this character should have some skill with magic as well as hand-to-hand abilities and comfort with firearms. That pushed me into playing with Chaos Magic because that's magic specifically channeled into hand-to-hand combat; it fulfilled two requirements at the same time.
Restrictions are good because they force us creative types to think in more imaginative ways. The results are characters that wind up being more memorable over the long term. Having a set of mechanics in place limits us in some ways and might prevent an exact implementation of the character that first put a twinkle in our eye, but it also means that what we eventually play is more unique.
You're not fighting against limitations; you're working within them. And in a lot of ways it works out better than getting to do whatever you want.
Leave your own stories of working within mechanical limits or just general discussion in the comments below or mail them along to firstname.lastname@example.org. Next week I'm going to dip back into professions with a discussion of a more mercantile pursuit. The week after that, I want to talk about characters you like compared to those you enjoy playing, which might not always overlap.
Every Friday, Eliot Lefebvre fills a column up with excellent advice on investing money, writing award-winning novels, and being elected to public office. Then he removes all of that, and you're left with Storyboard, which focuses on roleplaying in MMOs. It won't help you get elected, but it will help you pretend you did.