So the UK government had a plan that would have been good for cyclists and what if they didn't oppose it and restarted the bike programme as part of postwar reconstrutions?
Or like the Netherlands? Hey, wait a second...
Anyway, whether or not people would "like to own cars" is largely besides the point of the actual question of the OP. After all, sidewalks became much more common after World War II even though people were walking less. It's quite possible for a government to take action to benefit bike riders even if bike riding is declining, perhaps because it is trying to halt that decline or perhaps because it is more focused on recreation than transport.
marathag
Banned
An initial surge for trails that few are using by 1952 would not continued by future governments.
Would be derided as a boondoggle, wasting scarce resources and money on a failed program
Even into the 60's most people got to work by public transport, on foot or by bike and almost no one was taken to school in the family car so the cycle tracks would have been used.