The mistake is in trying to
understand the business case.
There is nothing to understand! The business case is the aggregate of what people actually do. There is no proper procedure that's actually followed at the ground level. Workflows are emergent and in constant flux. In this environment, the role of a dev should not be to build internal products, but to deliver internal hacks and ad-hoc solutios, maintain them, modify on the fly, and keep it all documented.
I.e. done right, it should be not just possible but completely natural for a random team lead in the mail room to call IT and ask, "hey, we need a yellow highlighter in the sheet for packages that Steve from ACME Shipping needs to pick on extra evening run, can you add it?", and the answer should be "sure!" and they should have the new feature within an hour.
Yes, YOLO development straight on prod is acceptable. It's what everyone else is doing all the time, in every aspect of the business. It's time for developers to stop insisting they're special and normal rules don't apply to them.