Why are there no ground targets in arcade battle?

Originally posted by Ciaran Zagami: I just wanna use my bombers ffs

It depends on mission you are in.
In majority of them, you will find at least some ground targets. But there are some without it, when your task is to gain control over airspace.

Originally posted by Ciaran Zagami: I don't wanna do airspace battles at all why is that not an option

Because mission you play is random. You can take more than one aircraft in Arcade Battles and that's the one of the main features of this mode - use it :)