I would have thought it 100% the other way ’round, David: the public cloud is oversold and often the wrong choice
But that it doesn’t have to be that way 😉
As for your statement that “private clouds have indeed been a path for vendors to sell more hardware and software” the operational realities of how physically the private cloud is delivered (yes, physical: it is all on the ground somewhere… nothing is really just off in the ether) belies your statement.
See, it is not always separate hardware. Separation can occur logically… there is a subtle but significant difference and it is all based on, defined from and the commercial realites calculated on the actual requirement.
A similar and related misunderstanding that consistently confuses the business / technical relationship (creating more CIO v CTO arguments than could be imagined) is that of virtualisation…
Business view: it is a single blade running multiple instances of a machine so we should pay for a single computer
Tech reality: yes, it is a single blade running multiple instances of a machine but each of those virtual machines requires software licenses, needs to be monitored and managed as though it were a separate machine. It costs less physically but not from a process perspective