Why should autonomous taxis be expensive? The whole point of them is to take away the most expensive part of the cost of taxi operation (the driver). In addition, the fixed costs of operation would be split amongst a large number of users. As a result, it should be less expensive than running your own car. That does sound on the face of it catastrophic for buses. One of the few advantages that UK buses enjoy is the avoidance of parking costs and hassle, but that is eliminated by using taxis. Road pricing will probably be essential when automated cars and taxis become the norm. That may be necessary anyway because of the need to replace lost revenue from fuel duty.
Certainly there would be no point in rural buses when automated taxis operate but that could be good news overall for buses if you have urban road pricing. Frequent high capacity autonomous buses from the edge of towns could be fed by autonomous taxis from neighbouring villages, meaning less need for your own car in rural areas than now.
Wealth doesn't automatically mean people stop using buses. The richest country in Europe is also the one where street public transport (bus/trolleybus/tram) has the best reputation and has the best modal share for such modest sized cities. The wealthiest city in the UK uses buses the most, even in outer London where the barriers to car use are nothing like they are in inner/central London.
Arguably, much of the innovation in the UK has come from London with the rest of the country following years later, if at all. For example, low floor buses, Oyster cards, contactless, real time information at bus stops and online, next stop announcements, electric buses, flat fares and the Hopper fare. TfL has been able try radical things out because its political leaders have demanded it, even if the Mayor's ideas are sometimes deranged, and TfL has historically been able to take the financial hit if it goes wrong. Whereas outside London is generally characterised by extreme conservatism and risk aversion because of the need to meet short term financial targets.
In terms of costs of taxis, I meant the capital cost. Presumably the number of taxi vehicles required to satisfy the peak requirement would always have an up-front capital cost greater than the number of buses required to satisfy that same requirement. For that reason alone, surely a taxi fare will always be more expensive than a bus fare, except in areas where the peak requirement is only a handful of passengers.
In terms of wealth, I don't know about the European city you refer to. But London as well as being the wealthiest city in the UK also has a large number of areas of "multiple deprivation". In terms of raw numbers, because of its size, it is therefore simultaneously the poorest city in the UK at the same time, paradoxically. I don't know London well enough, but my limited experience is that the main users of buses in London are a less well off demographic than tube and rail.
Oyster is certainly an innovation TfL and its predecessor can take credit for, but the ITSO-Compliant Smart Card platform that the public sector mandated for the rest of the UK shows that innovation by dictat isn't always best. And contactless is obviously a function of Visa, Mastercard and smartphones rather than something a politician has introduced. As for the other things, they are exactly what I meant when I referred to the "bike shed effect". This is where a committee meets to plan a nuclear power station. They spend 10 minutes talking about the design of the power station (because they don't understand it, and even if they did, there's nothing useful they can add) and two hours debating what colours and designs to put in the bike shed because this is something within the experience of the committee members. Bus fare structures and bus stop information displays are not radical innovations.
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On the speculation for the future, I wonder if the Exeter Minibus experiment will get dusted off and tried again, combined with some sort of demand responsive element? I suspect even today it would be possible to use an algorithm to work out how to plan buses in real time according to the likely demand, actual demand (if people had a smart phone app and pressed a button saying "I intend getting on a bus in the next ten minutes"), traffic conditions, etc. That sort of thing is only going to get more accurate in the future.
I can press a few buttons on my phone and get pretty much anything I'm realistically likely to want delivered to me by tomorrow - and for some items even today! That would have been beyond comprehension only 20 years ago.