Might want to look up the history of sidewalks a bit. TL;DR: it can be argued that the existence of sidewalks is a concession that roads are only for cars, where previously they were for everyone, including pedestrians.
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Unless you're defining "roads" to mean "not sidewalks", then almost by definition the statement "roads are only for cars" is false, because sidewalks are part of roads, reserved for pedestrians, and therefore roads aren't only for cars. The fact that there are reserved lanes for a particular type of traffic doesn't imply there was some sort of "concession that roads are only for" some other type of traffic, any more than bus lanes, HOV lanes, or bike lanes imply that pedestrians are getting pushed out.
From wikipedia:
"The primary features of roads include lanes, sidewalks (pavement), roadways (carriageways), medians, shoulders, verges, bike paths (cycle paths), and shared-use paths. "
Emphasis mine
>and why should they? In sensible countries walking in the general traffic lanes of a regular street is be fine.
I don't know what "sensible countries" you're talking about. Sidewalks are hardly some sort of concept exclusive to car-centeric America. Even bike/pedestrian friendly European countries have separate lanes for pedestrians, with some very limited exceptions such as during festivals/events.