Most of the time when people bring up these costs they have no experience with modern server hardware, and hosting. You can have the server shipped directly to a colo, you can file tickets with the provider to have it plugged into your power bar and your network, and you can connect with your IPMI client and set it to boot from your PXE/bootp/tftp server to get an install image.
With a well-configured setup, you have a one-off cost to set up your firewalls, wire-up the switches and power bars, and set up a server for the rest to network boot off, and the rest of bringing up your servers is near automatic and most management can be done remotely via IPMI or similar.
It's not the 90's any more.
(this is a question disguised as a statement, since I'm interested in your opinion)
Poorly managed old managed setups also probabl burned a lot of more experienced people. E.g. if you had to fill in stupid forms and request a server weeks ahead, odds are cloud equals freedom in your mind, even though a well run infra setup could offer you to spin up container workloads and leave dealing with adding capacity as a background concern developers don't need to think about.
Personally, I recall well the time I had to call in to Yahoo's hardware review board, chaired by one of the founders (Filo) because the billing system I managed, which handled millions of dollars worth of transactions, needed a new database server - priced around $10k. There were at least a dozen senior people on that call.
If that was your experience of colo/managed servers/on prem, it's not unsurprising if you value cloud services far higher than their costs for the sake of avoiding that bureaucracy.
I'm working on tooling that I hope will change that, by making compute and storage on cheaper managed providers vs. cloud providers fungible commodities, but it's a hard problem.
Permissions in the cloud is whole other beast, especially in Azure. You can easily spend a week figuring out various managed identity issues.
As for time saving: I've noticed cloud engineers often build a huge contraption of Terraform, Ansible scripts then bots and processes around them. That is then where the focus and time goes too.
And with any software, it is never done. It can always be better.
Classic sysops is much faster in a state of "done, no need to touch it now".