I just completed a survey on the teacher's use of the piano in undergraduate voice lessons. This is a "soapbox" issue for me, so allow me to mount my soapbox.
As all singers are aware, there is a "singer stigma" when it comes to musicianship. We are looked down upon, very often for a good reason, as having lesser musicianship skills than our instrumentalist brethren. I am increasingly convinced that one major contributing factor to this is the lack of independence expected of us. S.O.P. in most voice lessons is *some* level of accompaniment, virtually at all times--in exercises, and especially in repertoire. As a result, students rarely sing unaccompanied, and therefore rarely have to face the particular challenges of that skill. Furthermore, when the teacher's attention is divided between monitoring student behavior and playing some percentage of the song, they are rendered less effective at both tasks.
My first instrument was the trumpet. My lessons took place in a room with a piano, but my teacher never touched it. That is of course not practical for singing lessons, as we must be furnished with starting pitches, etc. BUT, I have noticed a massive improvement in my students' pitch memory, a strong uptick in the level to which they prepare their repertoire, and an increased sense of musical independence / confidence since I started teaching almost exclusively unaccompanied. As their teacher, I have noticed so much more in their singing, and particularly visual information, since my eyes are no longer buried in the score.
I also have urged my students to practice unaccompanied. In school, I used to play the bass line as I sang. That's lovely, as it's a decent proxy for singing with a pianist, but again it divided my attention. When I started practicing unaccompanied, I noticed so much more that was going on, and I more closely approximated a performance environment.
So, teachers: I encourage you to nudge your students towards practicing unaccompanied. Not only will they learn their music more thoroughly, but when they do eventually collaborate with a pianist, it will be on an equal musical footing, not as a dependent. And maybe, just maybe, we can narrow the "musicianship gap" with our instrumental neighbors. One lesson at a time, together.