There a few ways you can limit student videos:
Freeze Topics for View-Only
Flipgrid does provide the ability for educators to freeze Topics and make it view-only.
Moderate to Hide Videos
Additionally, educators can moderate to keep student videos hidden. Now, any new student videos will be hidden from the view of others. Educators can choose to only make 1 student video visible.
It's also a great teaching moment to let your kids know if they don't follow instructions, they will lose participation points!