Start-ups use AWS because with $20k-$100k in credits you can do a lot for free in the first year, and after that the cost difference usually doesn't matter. It also looks great on everyone's CV.

Big companies ofc have other reasons like flexibility, needing less coordination in the company etc.

If there were no economies of scale it certainly would seem strange that it could possibly be cheaper to rent computers from Amazon than to run your own data center.

Renting servers from Hetzner is a lot cheaper than using AWS. If you get your uplink figured out then running your own servers is also cheaper.

Sure, if you discount the administrative work to keep them up it might be.

Operating AWS and the datacenters involves massive economies of scale. Writing the software that powers AWS - not so much.

Yes, but since most of us (I think, anyways) are working on Web-hosted software that stuff all matters. It also matters that an Amazon or Facebook has whole teams dedicated to developer tools, operations management, and so on.