The Romans were thinking in political terms; i.e. eliminating a rival and controlling the Mediterranean, Carthage was thinking in economic terms; i.e. saving money. Yous definitions are wrong; (a) politics is the art and science of governance; (b) economics is the science of resource allocation where resources are scarce and wants are unlimited.
Cool history, but both were operating on purely Political terms.
This is a very old argument and one that is worth its own rap song.
But wait....
“Let’s Go!!”
https://www.youtube.com/watch?v=GTQnarzmTOc