Well, in the Netherlands it was supposedly the reason for demands for safer infrastructure, which in turn led to people starting to cycle more.
> Google Maps gives different routes for bikes and cars.
It does the same in the Netherlands, but I guess that's for a different reason: often roads are one-way only for cars, and bidirectional for cyclists.
(It's not as bad as it once was, but it still has the annoying tendency to avoid the Sarphatistraat, for example.)
That's basically how I am. I live in the DC area, and luckily for me there's tons of really nice bike paths like the W&OD trail. I can easily ride 50+ miles in one ride here just sticking to these trails, and see a lot of different parts of the area. Or I'll ride on subdivision roads that are very low-traffic. But there's no way I'm riding on normal high-traffic roads around here; it's just too dangerous.
I think the helmets are a big part of this.
If you go around telling people, "Body armor required," then they are not going to feel laissez-faire.
The other side is the presumed liability on the part of the car. Cars have almost all the responsibility to ensure they do not collide with a bike in the Netherlands. That makes cycling more pedestrian, you can just go and overall not worry about things around you.
But I do think that helmets get more attention than they deserve. Oddly enough, among experienced cyclists, a helmet is just part of the equipment. You either wear one or you don't. But non-cyclists (the folks who "advise" me at my workplace), the helmet is the first thing they ask about.
Oh, one more thing, European roads tend to be in a lot better condition. I had a near-accident last week because I didn't notice a gaping hole in the road that would have sent me over the bars.
A lot of Americans also think it's too dangerous. It's an obstacle to getting more people on bikes.
When people at my workplace see me with my bike, or find out that I'm a cyclist, they beg me to be careful, promise to wear a helmet, and so forth. I have friends who are avid cyclists, but who limit their riding to dedicated bike paths or off-road trails, because they don't feel safe riding on the roads.
Just looking at pictures and videos, it's apparent to me that cyclists in the US and Netherlands have very different riding habits due to the differences in conditions. The Dutch seem so carefree. Americans seem to have a much more wary, defensive, and sometimes aggressive style, and may prefer more maneuverable bikes for a reason. You'd probably get used to it, as lots of us do.
We also probably have to pay more attention to planning our routes to avoid the worst of traffic. I know all of the dedicated bike paths and side roads in my town. Google Maps gives different routes for bikes and cars. Residential streets have lots of cars but not a lot of traffic volume. I actually encounter relatively few cars on my rides.
Much as I defend cycling in the US, I'd still prefer the Dutch environment.