You're absolutely right. I understand "peak car" as trying to get away from unreasonable car use. Like in the US where one has to use a car for trips that one could easily walk, if only there were sidewalks.
I think one of the major causes of "peak car" is that, as cars become saturated, alternatives begin to come online as cities try to relieve pressure -- and once those alternatives (sidewalks, public transportation, bike lanes, etc.) have a critical mass of users, they enter the public consciousness as acceptable alternatives, and they begin to have more resources poured into them. When your area gets adequate sidewalks, you can get away from unreasonable car use, and your use of the new sidewalks encourages more sidewalk construction, etc.
I think you're right that this is a factor. What it doesn't quite explain is the decline of car usage in European cities that have always had sidewalks and good public transportation and where cycling isn't much easier now than it was 30 years ago. There seems to be a cultural change in attitude too. Cars are not as cool anymore as they used to be.
I think many European cities have seen changes in the past twenty years. Better cycling lanes, easy bicycle rental, increased public transit density and availability (eg late at night).
Yes, I forgot about petrol prices, which have increased substantially.
I'm not so sure about infrastructure improvements, at least here in Germany. I have been cycling for more than 20 years, and the infrastructure has not changed that much. Some places have improved a bit (especially in the last 5 years), but some are worse too. I feel that the experience is largely the same here. It may be different in places like Paris or London, though.
I lived and cycled in London the last 3 years, and there is a steady drumbeat of cycling improvements at all levels. Whether it's the congestion charge, cycle hire scheme, bike lanes, or even physically reconfiguring junctions with an explicitly stated goal of improving bicycle safety, there are major changes happening there.
I'm not sure how much change is happing on the continent, but based on some stories I've seen, there are many cities pushing the envelope, I think even within Germany (probably depends on the city?).