They are deterministic, but timing attacks are a big deal. There were lots of practical key extraction attacks on RSA with nothing but timing, even on a network

They are deterministic, but timing attacks are a big deal. There were lots of practical key extraction attacks on RSA with nothing but timing, even on a network. You can also do things like forget input validation in ways that reveal key material, or reuse a nonce or IV in a way that breaks the whole system.