What will be the security risks if we persist "e" as part of schnorr signature=(r,s,e) and extract publicKey from signature at verification

Question

We know unlike ecrecover, it is impossible to get to public key given schnorr signature = (r,s) since rG = sG-eP . So, would like to understand what are the security risks,

if we say signature=F(r,s,e)

and get to publicKey at the verification? something like this P = (rG-sG)/e

Answer 1

There are no security risks to this since e is public anyway. Depending on how you are using it you probably want to make sure that e is consistent with R afterwards i.e. recompute e from P and R and m to make sure it is correct. However, it makes more sense to me to just include P directly instead of e.