Players owning multiple battleships is not a problem in my opinion. After all, they can only fly one ship at a time (Unless they have multiple machines and are very talented)
1 battleship per player is NOT a good idea, even by eliminating mutliple battleships you still aren't going to make them more rare. It just wont work that way simply because, every "1 player, with 1 bs" is going to fly their BS if that's what they want to fly.
I am a former Battleship whore (I won't say former cap ship cuz I still fly gunboats, religiously) and I know (and ask any veteran player here) that reducing the amount of caps per player is not going to make them more rare.... People like me would just pick the one that suits their taste the best and delete the rest. (Did I just rhyme?)
Anyways my 2 cents on that rule. It was an OK idea, props for trying.