They rarely sing live - this is partially due to the fact that they aren't the best singers, but their songs often sound awkward without the vocoder/auto-tune/various vocal effects.
They always sing "Jenny" and "Perfume" live, they sung a cover of "Super Jet Shoes" live, and they've sung "Baby cruising Love" live one time. (And there was one time where they did "Laser Beam" live, but it was just the verse and with a good amount of backing vocals)
wait. And before I thought they sang with background vocals. It's understandable because their music is electro/pop. But rarely singing live...? =/ Even in live tour? I've never watched Perfume's live tour tho.
I blame it more on the choreography. with a song like this and all the bouncing it would be more difficult to not sound terrible when singing it live (of course, I'm fairly sure in the first TV performance of this they were singing it, at least over a backing track; I can't find an upload of it anymore but it was on Music Japan). I wouldn't be so quick to say it's because the girls aren't good singers, because A~chan is definitely capable, if not Nocchi as well.
I have a feeling that they're going to push for more singing opportunities in the future.