It is mainly 2 things (at least when I did it when I had the DJ crew and we performed all 3 together):
1. Fun
For you and the audience. You can have more fun as a DJ when you know your buddies and you sort of react what everyone does and put your things into it. It is also fun for the audience as it is also a performance act as 3 DJs are juggling around, waving and cheering on the crowd…
2. Diversity
Of course the whole thing is more like a round robin (there can only be one DJ at the knobs at a given time mostly, unless you make a live mashup with 4 tracks, which needs lots of prep work…) but everyone adds something into it and so the set can get really exciting and take shapes that are unseen. It is all about igniting each others creativity.
So yes it can be great fun, but I would only do it with people who I really know well and/or who I think are on the same wavelength with me when mixing into a genre. (For example I could picture doing a deep/belearic set with Phil 😉 )