Probably 95% of students who take lessons don't end up performing professionally. Music will be something they do for themselves and their friends, and good accompanists are rare in many areas. If she wants to be able to sing with an accompanist with any frequency, her options are to marry one (my wife's choice) or be able to accompany herself. Of course music is still a great thing to learn, but the reality is that singers really need to be able to accompany themselves once they no longer take lessons if they are to continue practicing and performing.
My wife teaches both voice and piano. One of her projects even for beginners is to have them play a reduced version of the accompaniment independent of singing. This has all kinds of benefits, especially a deeper knowledge of how harmony and melody intertwine. The more advanced students play accompaniments for each other. Even though they don't perform classical voice literature while accompanying themselves, they can practice that way.
As far as dropping one, all the music programs at university level that I'm aware of require piano lessons for all voice students. Singers who can't play piano at a high level will find themselves handicapped, especially if they ever teach music.
Singing opera while seated is probably not going to fly, but there is a big world out there, and many teachers will at some point introduce musical theater or pop music into lessons. Those are great genres to play accompaniments in performance. If your daughter's voice teacher doesn't get to those genres, at some point she'll probably want to learn some on her own.
Finally, remember that as long as practicing is getting done, there's no rule against practicing anything you want "on your own time." If the teachers don't want to teach a particular song, it's ok to learn it as long as you use good technique and learn it correctly. Even at university level, much of the learning is self-directed, getting feedback on pieces you learn mostly on your own. If her teachers are open to hearing pieces she's learned and giving feedback once a month, that may be an option.