Many cities in Eastern Europe, Russia, and Central Asia have (or used to have) Marshrutki[0]. These mini-buses and passenger vans don't stop at bus stops but where they are flagged down. You press a button where you want to be let off.

I say some cities used to have them, not because they went out of fashion (though sometimes they did), but because a Marshrutka is a specific type of passenger van, usually an old one not subject to modern safety requirements for economic reasons. Many of the companies operating them have modernized, and they have low-floor accessible shuttle-style buses with air bags and seat belts, including for disabled people, but they still go their route, can be waved down to pick you up, and drop you off when you ask.

There has never been a similar mode of transport in any Western country I've lived in, though I have heard rumors, and apparently, some US states have/had jitneys. Norway may also have something similar in the western tourist towns, because I found buses drop you off where you ask. But perhaps it's a courtesy. UK companies have made some similar efforts[1]. Generally, such mini-buses are not needed in urban areas. But there are areas where either super quick travel from point A to point B is essential and walking to and from a bus stop is unacceptable (airport-rail links and similar), or where there isn't enough demand to run a proper bus service. These could benefit from a taxi bus approach.

Anyway, Marshrutki and their contemporary counterparts address all the issues you've listed.

P.S. The solution for scheduling is the free market. Operators compete for customers, flooding the streets[2] during relevant hours. There may be 20 uncoordinated mini-bus operators, but for the user, the overall experience is that they usually have to wait only a few minutes along the route before waving one down.

[0] https://en.wikipedia.org/wiki/Marshrutka

[1] https://www.bbc.co.uk/news/uk-england-merseyside-44614616

[2] https://www.alamy.com/fixed-route-taxi-minibuses-move-along-...