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We did this a lot in the early 2000's. At the time I worked for a company with offices in Bellevue and we put our own hardware in full sized racks at a datacenter in the komo4 building in Seattle.

Because of proximity it was easy to run over and service the systems physically if needed, and we also used modem based KVM systems if we really needed to reboot a locked up system quickly (not sure that ever actually happened!).

I'm sure customer owner hardware place in a datacenter rack is still a major business