You make a good point here, and mass transit has done the square root of bugger all to improve accessibility for a new generation.
For example: I live in the countryside and want to get a bus into town. Fair enough but sometimes the buses run late, and sometimes they run really late - like half an hour plus. I often don't have that kind of time to waste, especially not if it means standing or sitting around in the rain. Moreover, it makes the timetable a work of fiction, and in that case what's the point of the timetable[1]? The truth is that in many cases I couldn't really care less about the bus timetable: what I want to know is when the bus I need is going to get here, and I'd like to be able to track its location to help with that.
Be great if there was an app for that, but sadly there isn't (not where I live, anyway). I have a feeling the Swiss Post buses might support that, but I could be imagining it. Thing is, it's not very start-uppable as a concept: you need partnerships with any bus companies involved, you need GPS equipment in the buses, you need parternships with cell networks and good enough coverage that location and ancillary information can be sent back to base to be served up through the app, etc.
In town the bus stops have those TfL style boards that tell you how long until the next bus arrives and where it's going but, of course, you still have to go to the bus stop to get that information.
[1] Timetables do become more important when you have to make changes, or use multiple forms of transport and make them dovetail together, so I'm not actually advocating that they be dumped.