My 10th grade geometry/trig teacher did this to us. Confidence issues I had as a result of this class lasted many years. I got over it and have done well for myself, but I still have some resentment.
It is not clear to me that this is obviously a bad teaching method. It definitely accomplishes 'engaging the student'.
Personally, I enjoy having students come up to the whiteboard. But when we do so, I present it as the student at the board is a representative of the class. The whole thing is collaborative, and I have students who are sitting explain what the student at the board is doing.
What this means is that students who know what's going on are able to take the lead (when at the board), whereas students who are less confident can rely a bit on their classmates. The whole time, I stress "Look, we're learning new stuff and it's going to be challenging. Work together and you'll get it." This makes a different vibe than if we just sat and watched before I determine if the answer is correct or incorrect.
I don't use this for individual assessment, and I don't attach any guilt or shame. It's purely done to get students working in the Zone of Proximal Development and to get someone other than me talking.