I am reading about Schnorr signature (for example, from BIP-340) and I thought, what if we add instead of multiplying for $s$? So, in the signing process it will be
s = r + e + d mod n instead of
s = r + e*d mod n. Verification will be the similar: calculate $s*G$ and compare it to $r*G + e*G + P$ instead of $r*G + e*P$.
$(r*G,s)$ is signature, $d$ is private key, $P$ is public key, $r$ is random value, $e = hash(r*G, P, message)$
Probably I am missing something obvious but I still did not get why it will be less secure. Signer shows that he knows the discrete logarithm of something for which he needs to know the private key.