It's curious but unsurprising that privatization of public transport is considered an answer to congestion when existence of good (or great) public transport is the working answer one can find in many places around the world.
When I visited NYC two years ago, I was blown away by how unbelievably bad public transport infrastructure is.
The most flabbergasting thing was the absence of Metro ring lines around the center. The fact these have not been built, in 2025, when Metro transport networks in most cities are now over a century old, is telling.
IMHO the real problem is cars. The US still can't imagine itself without cars.
I live in Berlin center. The only reason for me to own a car is prestige. So I don't.
During rush hour any destination I go to, even outer city, would take me the same time by public transport as by car. At least.
During non-peak hours going by car can be from 25-40% faster than by public transport if you trust Google Maps & co.
But these estimates only consider travel time. When you add finding a place to park at the destination (and walking to the destination as the place may not be right in front) this shrinks to either negative numbers or max. savings of maybe 25%.
My average travel time is around 30mins by public transport. This includes walking to and from the station.
Why would I own a car to save maybe, on a lucky day, 5mins?
At the same time bike infrastructure is being improved. Lots of side streets have been declared bike streets, cars may only enter if they have business there (you live there or deliver something).
The city has enforced this with blocking off intersections on such streets with permanent structures that let only bicycles pass.
Big streets have bike lanes that are often separated by a curb or bollards from car traffic.
This makes it also less nice to drive a car. You can't use Waze any more to guide you through side streets to avoid congestion because these streets can't be passed through any more by car, only on foot or by bike.
Which means the chance of being stuck in traffic increases. When at the same time you have options to be there just as fast with public transport and almost as fast but more healthy and with less likeliness of being ran over by a car, by bike.
These ideas are not new. And there are many more things other cities do to reduce car traffic/need for cars.
If you think of private mini busses, the best examples IMHO is actually ridepooling, e.g. Volkswagen's Moia in Hamburg and Hannover.