This is what happens when you believe the private sector is the answer to everything. We reinvent the wheel one hundred times, and each time its more square than before.
There is often cases where the first class offer exactly the same service as the second class, people are just paying extra to not be with poor people.
They didn't reinvent anything, private small scale shuttle buses have existed since forever. If you don't have them in your city it doesn't mean that's a brand new thing.