For me, it's the chance to get away from the built in stereotypes of the breeds and houses that appeals. Things like creating a Malcubi warrior that is dreaded and fearsome, or a Hulk intriger. When creating these random demons though, I wasn't planning any part of the campaign for them, I just wanted a small stockpile of demons that are fully statted as a reserve. For that situation where the players turn a corner and meet someone you weren't expecting, and suddenly need an NPC.
I'm writing a city for the 5th circle, which I'm hoping to get accepted for Signs and Potents eventually, so that's where I'll start running.
As for how I'd start a group, I'll probably go for a clutch of first level demons who've all crawled out the spawning pits of a particular house at the same time and have grown up together. Means the party would have a degree of cohesion to begin with, before they start back stabbing and betraying each other. Also by limiting the group to a single house, it will force the characters to be a little more creative in their choice of breeds. for example Sturach would normally be dominated by Fiends and hulks, but if the entire group are Sturach, then we might see some more unusual breeds occur.