Disagree almost completely
If you look at the definition of public and private clould, your CIA example is a VERY narrow niche; and the bleeding edge hardware example would most likeloy be outside the definition of a private or public cloud as this would more likly be a purpose built environment outside the definition (e.g. dedicated massive scale HPC).
The fact is that the security, resilency, redunancy, and flexibility of the major publiuc cloud providers well exceed the majority of forture 500 datacenters (and have all of the data and certifications to back up that claim); perhaps this is the reason why so many have moved, or are in the process of moving 80% to 100% of their enterprise footprint to the public cloud. This is also why organizations like Salesforce and Workday, both that contain highly sensitive data, are in the public cloud.
As for the new products use case, the public cloud would be more cost effective and more nimble in EVERY case; especially considering that you must maintain, and pay-for, excess capacity that allows for the quick provisioning of the required compute. Further, if you only need a single server there is simple no way to compete with public cloud products like AWS Lightsail.
Private cloud use in the enterprise (outside the narrow CIA use-case) is, at best, a bridge to fill in the GAP during the move to the Public Cloud. As for privacy and security concerns; this is the domain of misconceptions and the uninformed.
Corporate data-centers and private clouds = "Buggy Whips"