OK, this is a total aside, but I wonder if nationality has to do with this.
I'm from the US, and cycling here has the perception of being like golf - it's a sport with very expensive equipment that you practice if you're an upper-middle-class white guy. i don't think ive ever thought of the sport as a "working class" thing, but I've definitely thought it interesting that the perception is completely different in say, Flanders.
I think the geography plays a part too. Bicycles are pretty much the primary mode of transportation in the Netherlands and Belgium because they are tiny countries with roads that were put in several hundred years ago and not designed for cars at all, so there's this treasure trove of great roads, paths and tracks connecting everything together that everyone can ride on all day long, both for training and to simply get around. Historically, I would guess that workers that couldn't afford cars probably bought bikes instead, so the bike becomes a symbol of the working class while the people riding them are using them as a substitute for cars and racking up thousands of miles, a perfect environment for the early elite cycling talents to grow out of.
In a lot of places in the US I get the feeling that you're tempting death if you want to go on a long ride. There seems to be very few good roads to ride on that don't also have heavy car traffic, because the entire infrastructure is much more recent and has pretty much been built exclusively around cars and trucks. For people who are dependent on cars and have to cover the costs and expenses that come with that, the bike becomes a luxury rather than a cheaper alternative.
I think cycling might be trending further towards the middle class in general as well these days. The money being poured into the sport at the professional level has ballooned in recent years and racing bikes and all the extra bells and whistles have increasingly become additional pieces of expensive luxury equipment to buy, whereas a decent everyday road bike could feasibly be used for racing previously, at least for people starting out in the sport at lower levels. It has obviously become a completely different sport to what it used to be back in the first half of the 20th century. It is worth mentioning, however, that the very first edition of Liege - Bastogne - Liege in 1892 (which makes it the oldest annual race still in existence, but far from the first race ever) came at a time when bikes were still new and expensive enough that mostly wealthy people had access to them. However, in the first edition of the Tour de Frace, only 11 years afterwards, Henri Desgrange failed to attract entrants until he offered every participating rider an allowance of 20 francs, the equivalent of what a factory worker would earn in a day. Hardly enough to summon the aristocrats. Admittedly, the prizes of 3,000 francs for a stage win and 12,000 francs to the overall winner probably also helped motivate people to enter. That first edition was won by Maurice Garin, who also rode the first edition of Paris-Roubaix seven years earlier and worked as a chimney sweep before becoming a professional cyclist. That profession, by the way, is also not something that would have summoned a lot of aristocrats, I suspect. In other words, road racing seemed to quickly have gone from a rich man's pastime to establishing itself as a venture for people who couldn't make better money doing something a little more comfortable, and given that the stages in the first edition of the Tour were over 400km on average and that one day races could be over 500km* long I don't think a more comfortable job would have been that hard to find.
*They also raced Paris - Brest - Paris, which was technically a single-stage event, but given that it was 1,200km long there's not a chance in hell it could be called a one day race. Also, humans are crazy.