Public transit agencies vary dramatically from city to city, but they are the ones who provide Google with data on their transit system's timetables. In fact, Google is the last in a chain of software and manual labor that creates and manages transit schedules. It's very hard to create software that captures all the nuances and variations in transit to create a one-size-fits-all solution.
The other tough part is funding - public transit improvements are often driven by grant money because the operating budget all goes to day-to-day expenses. And oftentimes the wealthier people who could make a difference in transit (e.g. SV techies) own cars or otherwise avoid public transit because it's so inconvenient, so they often don't notice the problems.