> Didn't companies historically own their own compute?

As group-of-cats racks, usually, which is a totally different thing. Way "back in the day" you'd have an IT closet with a bunch of individually hand-managed servers running your infrastructure, and then if you were selling really oldschool software, your customers would all have these too, and you'd have some badly made remote access solution but a lot of the time your IT Person would call the customer's IT Person and they'd hash things out.

Way, way, way back in the day you'd have a leased mainframe or minicomputer and any concerns would be handled by the support tech.

> I thought the whole point of the cloud was that the hardware had been abstracted (and moved) away and you just got resources on demand over the network.

This idea does that, but in an appliance box that you own.

> And then if the machine is designed, set up and maintained by a third party, why even go through the hassle of hosting it physically, and not rent out the compute?

The system is designed by a third party to be trivially set up and maintained by the customer, that's where the differentiation lies.

In the moderately oldschool way: pallets of computers arrive, maybe separate pallets of SAN hosts arrive, pallets of switches and routers arrive. You have to unbox, rack, wire, and provision them, configure the switches, integrate everything. If your system gets big enough you have to build an engineering team to deal with all kinds of nasty problems - networking, SAN/storage, and so on.

In the other really oldschool way: An opaque box with a wizard arrives and sometimes you call the wizard.

In this model: you buy a Fancy Box, but there's no wizard. You turn on the Fancy Box and log into the Deploy a Container Portal and deploy containers. Ideally, and supposedly, you never have to worry about anything else unless the Big Status Light turns red and you get a notification saying "please replace Disk 11.2 for me." So it's a totally different model.