Bus vs car is just a miniature version of hub-and-spoke vs direct flight. Outside of very dense cities (Seoul, Tokyo, New York, etc.), mass transit isn't a very good idea because humans care about trip latency. A lot.

That being said, there's probably still a place for busses during rush hour in a lot of places.

Humans care about trip latency, but there are different components. One person walking five minutes to a designated corridor may save ten people on a minibus three minutes on their trip each by avoiding unnecessary diversion. And this can add up quite a bit depending on how many passengers you are avoiding diverting for. There's a reason why (good) bus lines tend to be direct and on main roads.

The main reason why non-dense places don't see good bus service is because of labor costs. In developed countries labor is easily the biggest source of cost when it comes to a bus, so agencies will run one 40-passenger bus every half hour rather than three 15-passenger buses every ten minutes. Removing labor makes the latter scenario affordable, and if buses are coming every ten minutes average wait time is about five minutes, which is comparable to Lyft or Uber today in some places.

We are used to busses going at set times from set positions. Why can't I request a $STARTUP ride from A to B, at about 30 minutes from now and let them try to calculate a route based on who else is going now? You could run that when you get out of bed and see what comes up, so that by the time you had showered it would be clear when you could go and then you could make the go/no-go decision.

I mean today it is a no-go decision from be, simply because it takes a minimum of twice as long to go to work by bus as by my car, but with a smarter route, that may not be an issue.

How is that different than just... taking the bus?

The difference is huge.

To take a bus from point A to point B, I have to walk to point C, wait for the bus, get on, wait to be dropped of at point D, cross the intersection to point E, wait for a transfer bus, get on, wait to be dropped off at point F, and finally walk to point B.

With this system I call a cab, wait for it at point A, get on, get dropped of at point B. Rather than my time being fragmented into 3 periods of walking interspersed with 4 periods of waiting, it is just 2 periods of waiting, which makes it much easier to make use of the time. In my experience riding buses, only about a third of the time spent is usable (except for long distance commuter routes), while nearly all the time spent in a cab is usable.

Even if the shared cab took a bit longer than a bus, I would still choose it over a bus for the improved productivity / enjoyment.

Lack of pre-defined and centrally-planned route.

That doesn't seem like a positive. People like predictability. They know their drive home takes X minutes, give or take Y, which is a small number. Having a different route every day makes the value of Y a lot more variable.

There's another aspect to "predictability." Back when I was a bus commuter, it was comforting to see the same faces every day. Even without chatting or acknowledging each other, there was a sort of familiarity to the strangers.

Is that a good thing, though? In practice the lack of a pre-planned schedule means that rideshare vehicles have to divert to get to you, being as much as 10-15 minutes away, which is not much better than just waiting for a bus.

Quickly catching a bus that isn't going where I want to go isn't ideal either.

It can pick you up at your house.