Great thought! I will play test!
Just had another thought, if you wanted to eliminate dice, you could setup a rock/paper/scissors type game using those Units
Infantry defeat fighters/tanks, lose to artillery/bombers
Tanks defeat artillery, or other tanks
Fighters defeat bombers/tanks but lose to infantry/artillery (imbedded aa guns)
That type of concept anyways. It would take some thinking through , more than this post from my cellphone haha but would be possible!