Is it a surprise that different sports have different cultures?

In hockey you'd never see the sort of diving that you see in soccer. You'd be laughed off the ice.

In soccer you'd never see the sort of casual violence after the whistle that you see in hockey. You'd be kicked off the field.

If you weren't willing to play with people who will fake an injury, you wouldn't play soccer.

If you weren't willing to play with people who will take physical shots at you, you wouldn't play hockey.

if you weren't willing to be around doping... you wouldn't go into professional cycling.

So once a sport gets that sort of reputation, of course it persists. The reputation causes the problem, the problem causes the reputation.

Because road cycling is 95% pushing the endurance/strength of the human body to the limits. Most other sports are a combination of many different skills. Road cycling is mostly about pushing the pedals as strong as possible for the duration of the race.

There's plenty of inspection in motorsport to make sure the cars are conforming to regulation too. Boxers gets checked by the referee before the fight, runner's aren't allowed shoes with a stack height above a certain threshold, etc. Cycling has had high profile doping scandals, but plenty of other sports have more doping but without the scandals. There's not a single bodybuilder or strongman that aren't doping for instance, and it's not even a secret. Plenty of athletes talk about how they make it through the season or individual games by injecting painkillers, cycling has a total ban on all injections.

Motor doping is not a realistic issue, there has been one cyclist getting caught in 2016, and that was in cyclo cross, not road racing. It's just not happening on the higher levels. For instance, this years olympic road race course is 273 km long with 2800 meters of climbing. Even if you could hide a motor and battery from the inspection and other riders, even if a team would be willing to risk their entire future if they got caught, even if nobody in the entire team would say anything, you're only going to fit a very small battery inside a road bike. For most of the 273 km it's unnecessary weight, so even if it was possible to get away with, which I don't think it is, would it even be a net benefit? I doubt it.

Well, the reputation comes directly from a few big scandals in the past - Armstrong/US Postal most obviously.

More generally, it’s obviously an ideal sport for some forms of doping given it’s based around extreme endurance. But there’s probably also lots of doping in other appropriate sports - running has plenty of history, swimming, biathlon, cross-country skiing, etc.

It's harder to hide the motor in gymnastics

Less variation at the top. The bike has a sort of normalizing effect. But the mechanical advantage also means minor cheating benefits get multiplied.

It's because the US' big star was caught doing it, so American media tries to project an image of it being normal in the sport. Same thing as those Soviet weightlifters. The actual prevalence is surely no different from baseball or tennis or what have you.

It is a sport where the race outcome is mostly determined by a rider’s max power output. And the max power output is in large part determined by genetics. Going beyond that max requires some “assistance“.

Pro cycling is very much a middle class sport, people are willing to put a lot of money into getting better beyond just what they themselves can do. A $5K bike is only the beginning.

At least for this type of cheating: cycling equipment is competitor-supplied.

Professional gaming tournaments that don't issue/mandate equipment have this issue as well, professional paintball has had this issue, etc.

in the usa most of the other sports allow doping