Does this simple signature scheme work?
This signature scheme doesn't even provide UF-KOA security.

The attack is simple: When you want to forge a signature for a message $m$, given a public key $P$, simply compute $h=H(m), h'=h^{-1}\bmod q$ and $S=h'\cdot P$, with $q$ being the order of the subgroup generated by $G$ (usually the curve order). $S$ is then your forged signature for $m$.

This works as:


We can efficiently compute the order of a curve.
We can efficiently find modular multiplicative inverses.