When I was still a singing student but working as an accompanist at the same time, my old teacher told me that I shall never play accompany for my own voice students at exams or competitions once becoming a teacher. I couldn't understand at the time but always remember and follow what she said.
Now I really understand why. Students need to have the experiences to work with different accompanists and learn how to lead.
My students always said that I play better than any other accompanists. That is not true. They are just used to the way I play and feel more comfortable when they are singing with me. Different accompanist brings different ideas and styles to the song. I always tell the kids to do exactly the way you want to sing it and good accompanist will follow.
These days there is less and less chance to work with accompanist LIVE. We used backing tracks for exams and concerts because it's easier and cheaper. However the more you work with other accompanists the more you learn how to lead.
When you can lead comfortably and own the song, your stage presence and performance will be impeccable.