You are assuming that there is no better way to define the schedules, no better way to communicate bus location, and no better way to start buses on time than what currently exists.
There are two sides to on schedule performance - what the bus does, and what the schedule says. You are probably right that the bus can't move any faster just because it is private. On the other hand, I bet a tech savvy company can do vastly better at predicting what the actual bus schedule will be as well as communicating any deviations from the schedule in real time.
> On the other hand, I bet a tech savvy company can do vastly better at predicting what the actual bus schedule will be
It's mainly traffic issues, or a single wheelchair/baby carriage clogging up the exits and requiring more time than anticipated. It's hard to make useful predictions for that.
> as well as communicating any deviations from the schedule in real time.
The municipal public transits in many European cities already have real-time schedule updates (and replacements) delivered via smart phone apps and digital signage posts at the bus stops. Big IT (I think Siemens, e.g.) has been offering and deploying solutions for this for years now.
There are two sides to on schedule performance - what the bus does, and what the schedule says. You are probably right that the bus can't move any faster just because it is private. On the other hand, I bet a tech savvy company can do vastly better at predicting what the actual bus schedule will be as well as communicating any deviations from the schedule in real time.