I think there are different factors. One is that doping in cycling had big media coverage, especially in the 90ies to 2010s. Media uncovered that basically everyone in the race org knew that doping was involved. See for example Cofidis: https://en.wikipedia.org/wiki/Cofidis_(cycling_team) This adds to the perception that cycling is very prone to doping.
Whether it is so more than other sports... I don't know. As was mentioned before, in cycling as in other endurance sports, doping can push you very far. Then there is the way the whole sport is organized. In the tour de france, privately sponsored teams compete against each other. I think this is very different to, say, a world championship. A country or trainer may have the interest of pushing their athletes beyond what is legal. But in a privately sponsored team, the pressure could be much higher.
Not sure your last statement is necessarily correct, just think of the massive doping in the former soviet union. The prestige gained by countries due to e.g. the Olympics regularly causes people to use illicit means.