But that's the thing. A senior engineer is also costing a business ~$100/h (all in) so even if you accept that there will be a fair amount of waste (misconfigurations, devs spinning up boxes and then forgetting about them, PoC projects never torn down, etc) it can still be a net-positive proposition. People always want to compare the cost of compute/storage/bandwidth but that isn't really the value proposition. Of course you are going to pay more for cloud-hosted infra than for equivalent infra in a colo or on-prem DC. But I used to spend hundreds of hours a year doing random busy work to deal with on-prem infrastructure. Need a new server, put in a ticket and when the ticket gets no response follow up with emails and finally setup a meeting to discuss with the ops team. Need a new firewall rule, same deal.

Have them build an s3 attachment service and just let finance know you are spending $X/yr and you have ideas for streamlining IT support that would eliminate the cost.