Both Amazon and Digital Ocean do have dedicated CPU instance types. The prices will make your eyes water. (I have not used the other cloud providers, so I don't know what they're up to.)
Obviously selling CPU on a time-sharing basis is a good idea; most customers aren't maxing out their CPU 24/7, and this lets them pack more customers into fewer machines. (RAM is the killer, though, and you'll see that at every cloud provider, RAM is really what you pay for.) But when you compare these prices to what a CPU costs... it starts to make you think.
My last job really warmed me up to the idea of just running my own servers. All our workloads were containers running in Kubernetes. With Kubernetes, I don't care about individual computers anymore. If one malfunctions, workloads can be easily moved to another computer. All the machine setup work is made machine readable by building containers and authoring Deployment objects, so there is no mental investment in a particular computer or disk image that you get from logging in, installing Debian, screwing around with files in /etc for an hour, etc. Basically, any sort of maintenance involved with physical computers no longer concerned me; repairing a hardware failure basically meant just repairing that hardware failure at my leisure and then moving on.
Combined with this was the fact that we were an ISP, so we had a datacenter, power, networking, and all that the floor below our office. I eventually convinced myself that for a month worth of AWS fees, we could have 10x the computing resources and 10x the bandwidth for a one-time cost. Nobody was motivated to hand over the credit card and let me build the cluster... but for me, running dedicated servers went from "thing that only Google does" to "why isn't everyone doing this!?" It's just not that expensive. And, consumer-grade hardware is really good these days. I drooled over the fast builds we got from a c5.4xlarge AWS instance. A consumer Threadripper build would blow that out of the water for about the cost of 6 months of AWS. (Amazon pays the Intel tax. You don't have to, though.)