Character development. How much does Gren spend on getting food for his team? How much does it cost to maintain his equipment and hobbies? How does he get all these neat gadgets and thingamajigs? How much does he send back to his folks so they could live comfortably? As entertaining as living on a sitcom budget is, Lien has other uses as well. As Kabel mentioned, not all of do the contests nor do missions occur fast enough to give us a steady stream of credits. I'd prefer to use Lien to purchase minor or secondary equipment. Grenades, dust, medical equipment, sentimental nicknacks. Otherwise I'd take liberties to make sure Gren is armed with not just the God Eater, but other misc equipment like various tactical equipment like grappling hooks, explosives, and additional augments to his cybernetics. Sure I could pay credits for these, but some of them are rather minor, and I'd rather not spend a whole credit for essentially a zoom in function and perishable goods.
To me the issue with credits is that they're way too expensive for moderate purchases. It'll be like having to spend $100 every time you want to buy a pocket knife or a crowbar.