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

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 saysignature=F(r,s,e)

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

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