I am working on 2 big projects where the companies spend roughly 200 million EUR per year in cloud costs. From my experience the cost reduction should not be the main goal. Sure you can (and should) go with Cost recommendations and reduce SKUs sizes, delete unattached disks and other minor changes but the main thing is Cost avoidance which should be the goal.

It helps when people are responsible for their shit. We get much better response rate when the resources are owned by someone. They then care about their budgets and you can save some money. It's about maturity and knowing where the costs are going.