In any case, there are plenty of examples in the US as well. Private education can successfully compete with public education, despite great structural disadvantages (private schools literally have to compete with free product). Using EBT at Walmart works better than government cheese. Section 8 housing works better than the projects. VA hospitals are not exactly preferred to regular ones by the public.
In general, in the US, the government doesn’t directly run too many things other than the regulatory agencies. Most of what it does is already outsourced. The US government doesn’t build infrastructure, doesn’t design or build military hardware etc., and most people (not just the straw man Ayn Rand fans in your head) would recoil in horror at the idea of government directly hiring people, buying materials, and managing operations.