Do they? I mean, technically the US gov't leases a ton of desktops (not great for scientific/technical computing), and they own a few supercomputers for specific needs (national defense, weather), but mostly they fund modest computational centers in academic environments. Before cloud, I worked in grid, and grids strapped together the many academic and government clusters, mainly for embarassingly parallel workloads.

I don't think the government has shown itself to be a particularly skilled operator of large computing environments compared to the large cloud providers.