For me, a big part of playing in a band is musical development. I strive to be as complete a musician as possible, and live performance is my real world, full speed training ground. If you're playing in only one band over time, it becomes easy to get stuck in a role. Playing in another band is a low-drama way to overcome that.
I really enjoy playing many styles of music and instruments, and it's real hard for me to find a single band to cover what I want from music. One thing I like about playing at church is that I get to play an acoustic fretless bass, which is something that wouldn't work for most of the cover gigs I do. My church doesn't play Gospel, so I relish a chance to sit in at elsewhere and 'do church'. If I do a sub gig, I rarely get a chance to sing lead, so I do acoustic shows to give me a chance to sing some more. I love getting called for a one-off Blues gig, because there's a chance for me to blow some harp and play guitar without having to commit too much time beforehand. I did a short theatre gig, and it gave me a chance to polish up on my reading. The things I want to do musically seem endless, so I love the endless possibilities from working with multiple projects.
Not only instruments or style, there's the role as well. I've been a bandleader, a band member, a hired hand, and a sub. I can certainly say that I learned something from each role that helped me to better understand the whole picture. I learned what I liked about each, and what I didn't. I learned how to be better in each role from seeing from another perspective. I honestly have to say that this didn't just improve me as a musician, but as a person in general. There's so many real life lesson learned from each role in a band.
And then there's the people. I'm a relatively extroverted guy, and I like playing with different people. I don't expect everyone to put the same priority towards music as I do, so I tend to be cool with the amount of effort that people put in because I can meet my musical needs elsewhere. No need for me to put people in a pressure cooker or drama situation. I can work around you, and still meet my musical needs. Aside from priorities, there's also personalities and styles. There's some people I just enjoy a chance to hang or jam with. Different musicians bring out different styles of playing in me, and I get a variety of cool synergies.
In short, doing the multiple band thing really improved my musical development.