Can you provide a citation? To my knowledge, the Archive does not use Amazon's S3 storage system (which they refer to in places as "S3" [1]), only they're on their own internal storage system [2].
To the best of my knowledge, the Archive has it's own machines to store data. It is an Archive and one of the principles was to have the know how to preserve data even if the cloud providers disappear.
> How does archive.org make money?
Donations (https://projects.propublica.org/nonprofits/organizations/943...)
> I imagine their storage costs must be quite high.
No, they aren't. Building and hosting your own storage is cheap. Same reason Backblaze and Dropbox built their own storage systems.