Supersonic missiles unlikely to penetrate battleship armour?
Soviet Union's first supersonic antiship missile P-270 Moskit.
https://en.wikipedia.org/wiki/P-270_Moskit
Speed ~1000m/s. Weight 4500kg. Energy 2259 million joules.
16" Mark 7
Speed 762m/s. Weight 1225kg. Energy 355 million joules.
Moskit is armoured against 30mm autocannon fire and can even tank a direct hit from 5 inch gun. It's literally armour piercing missile intended to withstand barrage of US fleet CIWS fire.
During a test fire missile with dummy warhead (so just kinetic energy) split the target ship in half. The target ship was large vessel. Unfinished early cold war cruiser if I remember right. The missile was rated by Soviet Union for sinking 20 000 ton vessels. It could sink carriers easy but Soviet Union had carrier killer antiship missile, Kh-22.
Moskit would penetrate battleship armour with ease. Maybe not sink it but it would cause a lot of damage. Battleships were build to withstand a lot of punishment afterall.