I've thought of this before, and it makes a lot of sense! Sometimes one can write a seemingly "correct" proof, but there may be gaps in the argument that isn't obvious until someone else looks at it. Heck, even professional mathematicians get it wrong sometimes.

Another thought I've had to help solve this issue is to supplement learning mathematics with formal methods. Using something like Lean, one may make a mathematical argument that is truly airtight and the student may feel at ease knowing their understanding of a proof is complete. This could be the feedback loop that you mentioned.