Public transit is a great example. Pretty much every attempt to privatize transit worldwide has resulted in, if not failure and subsequent deprivatization, at least higher prices and worse service for the people using the service.
The interstate highway system, which replaced a complex system of partially privately owned roads, is another.
In most countries, healthcare is another great example. And arguably education as well - public schooling produces generally pretty good results worldwide for not that much money per student, and outside the US, higher education is often public and incredible value for money.
US public transit is a finacial disaster far beyond any other country.
Road maintenance is normally cheaper/faster with private.
Healthcare is a can of worms but you could be right. The real problem with public health is what happens when these gov can't afford it anymore. US is likely in the wrong now but I want to see the results 50yrs from now when social spending cannot keep up with rising costs and decreasing taxes in EU (population collapse).