Is cycle sport encouraging uptake of cycling?

Also note that those more progressive cycling countries are devoid of any history of auto manufacturing.

In the US, the post-war highway system construction by Eisenhower was largely heavily driven/encouraged by the automotive sector. They already had the government contacts after their heavy involvement in manufacturing during WWII.

Gobshite:

Cars manufactured in Germany, a progressive cycling country compared to the UK and US: Audi, BMW, Mercedes-Benz, Opel, Porche, smart, Volkswagen.
Cars manufactured in France, a progressive cycling country compared to the UK and the US: Citroen, Peugeot, Renault, Bugatti (German owned)

And that's just some of the cars manufactured in those countries today. Ford also owns plants in both countries and both have over a hundred brands that are no longer in production today.

Belguim has over 80 brands to it's national history, two are still in production.
Netherlands has over 30 with four still in production today.
Denmark, 18 brands, one still in production

This is all information from Wikipedia so the true lists may be even longer.

Given the population densities in question, Western Europe could easily be argued to have a far greater and far richer auto industry history than the US.