Not everybody feels performing in public needs to be part of learning. I have nothing against those who prefer to play in private. Personally I tend to have a bias towards students who can perform for a number of reasons.
In my school days I learned violin. The school was semi-private. At the end of the year the people in strings & band classes would perform in groups for the parents. Partly to show the students made progress and partly as a fundraising event for school supplies (more as an obligation). Only part of the funding came from the local govt through the school board.
The past decade I've been playing violin with a music group. I have musical friends who sang in a church choir. At a typical Christmas party we'd sing carols. Everybody is expected to participate. The majority who don't play an instrument would join in the singing.
In my teenage years I have gotten used to performing. Over the years I met Suzuki & Yamaha people who are required to perform in a year-end recital from 1 level to the next and people who passed conservatory levels but never performed except in front of their teachers.
People often say they'd practice a piece to a performance level but where do they perform? In front of their teachers. If someone can play a piece in front of a teacher, he/she should be able to do the same at home in front of a family member or friend. I don't mean in an auditorium with 50 or 100 people. Even being able to play the 1 song you really love.
About 5 years ago I was at a gathering. A mother asked her kids who learned piano and passed conservatory levels to play something. There was silence in the room (nobody volunteered). To be fair, nobody touched a piano after their last piano lesson /music exam years ago. There are people who treat piano playing like academic exercises. Some would only practice for a teacher. Once they stop taking lessons, the piano just sit at home like a piece of furniture. I play music for stress relief and always find interesting pieces to learn. The ones I played yesterday I'd be able to play on a public piano. Maybe not the whole song but at least a few lines which isn't too unreasonable.
2 years ago I heard 2 people who took piano / violin at a gathering. The teens passed their ABRSM-8 and played with a small ensemble. Grandma said they're talented and wanted them to play something. They both picked pieces their teachers assigned. My impression was that they have confidence performing in front of people but the ones they chose weren't super technical. Passing level 8 is already an accomplishment in itself.