I guess there's another in-between step buying your own hardware, even when merely "leasing individual racks", and EC2 instances: dedicated bare metal providers like Hetzner.
This lets one get closer to the metal (e.g. all your data is on your specific disk, rather than an abstracted block storage, such as EBS, not shared with other users, cheaper, etc) without having to worry about the staff that installs the hardware or where/how it fits in a rack.
For us, this was a way to get 6x performance for 1/6 of the cost. (Excluding, of course our time, but we enjoyed it!)
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