Yes, they run in the cloud, see e.g. https://cloudrun.co (disclaimer: my side-business), but others have done it as well, for a few years now. On dedicated, shared-memory nodes, it's no different from HPC performance-wise. It can be even better because cloud instances tend to have later generation CPUs, whereas large HPC systems are typically updated every ~5 years or so. But for distributed-memory parallel runs (multi-nodes), latency increases considerably on commodity clouds which kills parallel scaling for models. Fortunately, major providers (AWS, GCP, Azure) have recently started offering low-latency interconnects for some of their VMs, so this problem will soon go away as well.