That's a great idea! I knew a guy who played chess that way, too, back in pre-Internet days.
Besides classic Battleship, I also had Sub Search, which was played on a 3-dimensional, 3-level board. Both players had surface ships, on the top level which was the surface, and 3 submarines that he placed on the other levels. Each player had mines that he could place, too.
I also had Tank Battle, which pitted small-scale Panthers against Shermans--Fireflies, I think--with Hueys for aerial support. There were also HQ, fuel dump and ammo dump pieces.
And I had Carrier Strike!, which gave you four vaguely-Essex-class carriers, one side with Avengers, the other with Kates. I painted the one pair up like IJN carriers, and I painted the aircraft. Basically, you just launched torpedo attacks on your opponents.
They had a Chopper Strike game, too, but we didn't get that one.
When I was older, I thought it would be cool to play a wargame, using all of those war games.