I always liked the idea of competition, but Osu! already gives that without having clans.
The idea of a clan, from what i can think of it if implemented inside Osu!, will be mainly for doing Clan wars.
Other than that, clans might be pointless.
When playing an mmorpg, clans are usefull because you get to quest with your clan members and get benefits out of it, but we don't have that here.
I think what Osu! aims, is to have a solid and friendly community. Competitive as it is yes, that's what the rank up is for, but if clans were implemented, there might be heartfeelings.
There will always be the friend that wanted to be with you in the same clan, but he can't because his skill ain't high enough to meet the clan's requirement for example. He will most likely feel bad about it.
Don't get me wrong, im not saying i wouldn't like to be inside a clan, it might be fun. Clan ranks and such.
But im just saying it might affect the community a bit.