> Does any country have any success stories?
Yes, but it depends on how/why things are done. You don't hear about the successes because it's not a story worth telling.
Charter schools are a good example. They have mixed success when deployed. In many places they're deployed by right-wing politicians primarily to weaken public schools (and their unions). This can be done via a variety of ways, such as letting the charter schools charge extra (thereby essentially subsidizing private schools), allowing the schools to "expel" problem children, thereby dumping the public system with them, etc. The result is usually a framework that isn't designed to actually make education better.
In some places (Sweden is a good example), charter schools were implemented by a centre-left government because all attempts at school reform failed due to a variety of reasons. The result was by most measures successful as the charter schools couldn't pick and choose kids, were still held accountable, and it resulted in the public schools having to stop fighting reform in order to sort of compete.
The Canada line in Vancouver (metro link to the airport) was build on time and on budget and is still run by a P3 company, as is the new REM line in Montreal. The incentives here were ONE company was given a contract with clearly laid out incentives and minimal political meddling after that (as opposed to other P3s where the government is highly involved and subcontracts, etc get doled out to connected firms, etc).
The UK car industry was mostly privatized, but judgement on its post-privatization failure mostly goes down political lines (eg should a government continue to subsidize poorly made cars in the name of employment). Same with most of the rest of industrial Britain, which under public ownership was uncompetitive in most cases. That being said, most would consider Rolls-Royce to be successful and was privatized in the 1980s.
BP's privitization was mostly a success, even with all its issues.
Canada privatized CN rail and it is now one of the most efficient freight railroads in North America.
Telecom privatization in the EU has mostly been a success (though one could argue that the EU has pushed for too much competition, which has meant that while mobile prices are generally very low, it has made it harder for companies to invest).
Many airlines outside of the USA were also publicly owned pseudo-monopolies. Flying is cheaper than it's ever been, even if no longer glamourous.
The TL;DR is of course it's a mixed bag and depends on so many factors. Many UK industrial firms were so poorly run under private ownership that they were so far behind they couldn't catch up and compete once privatization did happen.