I differ with you on the opinion about battleships being obsolete. Perhaps World War Two era battleships are obsolete and I’ll agree. But the role of a battleship in a modern naval fleet isn’t quite yet obsolete any more than destroyers, frigates, corvettes, gunboats, and submarines are obsolete.
I am not an naval architect and will not speculate on what a modern battleship would look like, how it would be armed, and etc. but the experience of the Gulf War should demonstrate that there is yet a place for a big gun capital ship in a modern navy.
I also think a modern battleship would be pretty damned cool !
The big gun ship can be replaced by a smaller ship mounting railguns.
Here’s something else to take into account.
Thickest armor on USS Iowa - 19.5 inches on the turret faces - 17” armor plate over 2.5” of STS steel.
Armor penetration capability of Russian Kornet-D semi-man-portable antitank missile: 51 inches - and that’s after penetrating explosive reactive armor.
Modern antishipping missiles are even larger, thereby having even more armor penetration capability.
The advent of the missile propelled shaped charge spelled the end of the battleship as it renders armor beyond a level sufficient to protect against small arms up to 5” gunfire irrelevant.