There's an explanation for the carriers in episode 7, it's pretty silly and amusing, but also matters for the overall plot. In general, they knew the premise was silly, so they made a silly world to fit it into and just ran with it.

And I wouldn't say it's all that moe, Kato. Not even if you ignore the original connotations of vulnerability moe has and just take it to mean cute girls doing cute things. Most of the show is made up of tank battles that focus on the actual fighting and tactics, rather than on the girls being cute during the battles.