The intention with increasing area of damage was to speed up killing squares, since you could attack more of them with a single attack.
I haven't considered this perspective before but you're right, it actually discourages players from attacking multiple squares at the same time because they might die before getting resources from them.
Initially I wanted to add an upgrade that would increase damage based on the number of squares attacked at the same time, so that the more squares you'd attack the more damage you'd be dealing but I haven't implemented it.
This is great feedback, thank you :)