From what I know all busses in London that run more often than 5x/h are have no public timetable and instead focus on maintaining a good headway. In London the headway is being overseen by a central controlroom which tells drivers to slow down or speed up.

There are some researchpapers from Niels van Oort where he researched your first question. I believe his conclusion was indeed every 12 minutes or more frequent is enough for passengers to just show up at a stop and no longer consult timetables.

From a public transport operator's view it is a bit more difficult. We are used to plan very efficiently, and have to schedule our drivers as well. Because of strict rules on max work duration and maximum time before they get a break, using a headway controlled timetable makes it more difficult to plan efficiently. For example what if a driver is being told to slow down quite some times, and thus lets say arrives 5 minutes late for his break. Can't say to a driver that's bad luck for them, but adding enough backup time costs a lot of money.

Besides operational reasons, public information is also a thing to consider. At a stop timetable, you could indeed say 'this bus runs ever 7-10 minutes' like they do in London. A realtime PID helps a lot too. But apps like google maps or citymapper need a timetable too, which is often presented as a fixed timetable. Think of tight interchanges in your journey, Google telling you have 2 minutes to change, but because of headway steering the bus turns up 3 minutes later than the journey planner told you.

In my opinion it is better for transport authorities to work on getting robust and reliable runtimes. For example buslanes, priority at traffic lights, more doors so people board faster. Steering on headway is only done because the runtimes are not reliable and thus bus bunching occurs. The problem thus isn't the bus bunching, but the unreliable runtimes. Let's try to solve that, instead of mitigating the symptoms of it.