The opposite, I don't understand why anyone would ever put up a server if they didn't have to.
It's not 'processing power' that's going to be the 'big cost' for most projects.
It's headcount and salary.
If you can materially improve the operating ability of your company, then a few $K in cloud fees is dirt cheap.
I used to work at a 'tech company' that made a physical product and our IT was abysmal. We had to wait weeks for our sysadmins to order blades, get things set up, there were outages etc..
If a project is definitely going to be 'a few linux servers and never more' - even then it would be cheaper and more reasonable to use virtual instances.
The time to 'roll your own' is when the infra. operating costs are a material part of your business.
For example, 'Dropbox' invariably had to roll their own infra, that was inevitable.
Similarly others.
That said - as this article indicates, it's easy to 'over do it' and end up in ridiculous amounts of complexity.
The Amazon IAM security model has always been bizarre and confusing, and the number of AWS services is mind-boggling.
But the core case of EC2+S3 +Networking, and then maybe a couple of other enhanced services for special case works fine.
I also object to what I think is a vast overuse of Cloudflare, I just don't believe that in most scenarios needing to have content at the edge really changes the experience that much.