This was in fact the status quo before public clouds became popular. Machine time was billed out by the IT department back to projects and departments, so even getting an OpenVZ host would require forms and approvals, and could take weeks if vacations lined up poorly. I assume many companies are still like this. Certainly my current employer is: if you really actually want on-prem compute or storage you can get it, but it's a slog.

IMO this is the easiest way to drive cloud adoption: tell PMs that the cloud is instant but on-prem takes weeks.