Whether or not students should do performances is actually a widely debated topic. Some teachers require recitals and competitions, other teachers never host annual studio recitals. Some teachers want students to learn and experience competition, other teachers wants students to never experience the horrors that can come from such experiences. The clear fact is, that being a good performer has little to do with being a great musician. Certain teachers see performances as add-ons to what a student really needs to learn. Other teachers see performances as opportunities to grow as people and learning to perform is an essential skill.
My view is this: there is nothing that can grow a student's ability faster and more specifically than preparing for a performance. To do a great performance, the student needs to know the true musical aspects of the piece (to feel the meter, to hear the melodies with their "inner ear", to expect what kind of cadences they are approaching, to understand each phrase), and also be extremely confident and fluent in their playing. Once a student has reached this level with their piece, they are truly ready for something more difficult. After they have performed and have done a wonderful job, the student has good memories of accomplishment and dedication to build off.
But the performance opportunities that I give my students do not begin with the bi-annual studio recital. I start with performances in front of the video camera in their lessons. Students learn such concentration skills by playing in front of a camera! Another opportunity is at the monthly group classes students attend. I always have a performance time, and students perform their most polished piece; at least that is the goal. A lot of the times, students feel so comfortable in the group classes that they choose to play almost brand-new pieces. There are some things I can't control! :) Students also do the Achievement Program and Michigan Student Achievement Tests. By the time they get to the studio recital, most students have done about 3 or 4 semi-public performances.
As a rule, I never put a student on a program who is not ready to play. This rule is in place so that no student ever has to endure that kind of experience, which can be crushing. I start planning what they will play on the studio recital and tests months in advance and always plan a "back up" piece (one that is much easier) for them to play if their actual-level piece is not ready. This way, they will always feel included and have a good performance experience. Of course, this can only work for recitals; for tests, I always choose their testing level very carefully so that not being ready is almost an impossibility. If need be, I do as many extra lessons as I need to give to get them ready.
In short, I believe that performance ability, although not essential for musicianship, has a huge effect on a student's ability, and I will always encourage it!