You have to do an apple-to-apples comparison though. If you're comparing a single colo'd machine vs a 3000-EC2 instance fleet with a load balancer, api nodes, database nodes (and requisite db admin team), and Kafka and DynamoDBs somewhere in there, then the cloud is going to be more expensive to manage.
Barring in-depth research (which I'd love to read if someone has any links), it's not clear on a 1:1 basis what's cheaper. Paying for someone's time to research hardware and talk to vendors, run POs for them, figure out where/how to install them (Equinix is expensive), and RMA hard drives as that comes up; versus not paying for that and instead paying a cloud vendor for that privilege. Throw on top a changing hiring landscape (how much 'sysadmins' cost vs 'devops') and it really depends on the size of this hypothetical fleet that we're trying to manage, and how complicated the backend of the site is. If there's no real backend to speak of, Cloudflare's CDN for static assets is going to be way cheaper, and available now, vs anything you could possibly build from scratch, that would maybe be ready in a couple months.