I've read that one reason to use a new address for each transaction is because it hides the pubkey behind a hash, so that even if ECDSA is broken and someone is able to derive my privkey from my pubkey it would still be impossible to spend the output of the transaction, since they would need to be able not only to reverse the hash but reverse it into a valid pubkey. Assuming that's impossible, and assuming people use a new address for each transaction, what would be the full security implications for bitcoin if ECDSA were broken? How much protection does hashing the pubkey give from broken-ECDSA attacks?
First, if ECDSA were broken, a lot of other things would be broken, like ssh, https and a bunch of other things, including banking websites.
Second, if nobody reused addresses, then yes, bitcoin would be protected by SHA256 and RIPEMD160. There is currently no known way to get a preimage of a hash used by either of those functions so your bitcoin would be safe. Again, this assumes nobody reuses addresses.
As far as how much protection this gives, it's hard to say because it depends on the exploit used to break ECDSA.