Just a few servers could be kept idle, not off, to enable a sub-second start-up time for some new work.
Even purchased on the used market, a decent server could cost $4000; if you spread that cost across 4 years, that's $80ish per month just to pay for the server, which is probably around your power / rent costs.
The costs are more stark if you're buying new, where it is easy to sped $10-30k for a decent spec server.
Don't buy a server to leave it turned off, you're wasting money.
Not all workloads are CPU-bound. Cloud providers have many servers for which the CPUs are idle most of the time, because they're disk-bound, network-bound, other-server-bound, bursty, or similar. They're going to aim to minimize the idle time, but they can't eliminate it entirely given that they have customer-defined workloads.