How bad is it to use the identity function as hash for ECDSA?
There is a way to generate forgeries for (EC)DSA when the hash function is not one-way:


Let $n$ be the order of the group, $P$ a generator, and $Q = aP$ for some secret $a$;
Pick arbitrary $\alpha$ and $\beta$ $\in \{0, \dotsc, n\}$;
$r = x \bmod n$, where $(x, y) = \alpha P + \beta Q$;
$s = r \beta^{-1} \bmod n$;
$h = s \alpha \bmod n$;
Invert $H(h)$ to get $m$. Since we are using the identity function here, $m = h$.


You can verify that $(h s^{-1}) P + (r s^{-1}) Q = (\alpha P + \beta Q)$, whose $x$ coordinate is precisely $r$. Therefore this is indeed a valid signature.