I would definitely call battery powered “nice to have” for me, but far from essential. I can think of two situations where batteries are very interesting:
a) when something is very compact and self-contained. Something you’d want to use on the road to make/compose/produce music, or to perform in situations where you don’t have access to power.
b) something that you can actually play while dancing/jumping around, so you don’t have too many wires in the way.
This said, I’m not really the jumping on stage kind of guy (the little I perform, I do in a pretty static fashion) and I rarely feel the urge to compose music in the wilderness (though I should try that once). Usually I can live with one more cable attached to whatever I use.
I can imagine situations where a) could be interesting in combination with playing live in places where you don’t have power, so you have use either go with acoustic instruments or something that is battery-powered. In this situation though, the instrument would also have to be equipped with a good quality speaker, that can deliver the necessary volume and cover the needed frequency spectrum to be able to be sound together with other instruments.
Which is where most battery-powered instruments usually fail.
The only thing where I really do need battery power is field recording, in fact I’d be really great if I could get the Field Kit to work on the go, with enough juice to drive the motors and all.
My main thoughts and concerns when buying something that has a built-in battery is: how long will it last – in terms of expected life – and how long will the charge hold? Can I get a replacement when it dies? Can I replace the battery myself? How much avoidable waste am I going to produce?
In general I don’t use batteries in instruments a lot. For example, I usually have the Volcas attached to the wallwart. The problem is, these batteries usually run out and you have to replace/recharge them, which is just one more thing to think about. Also, there’s really few situations where I really don’t have a power outlet close by.