Today whenever you see a winning professional cyclist on a podium, they're usually wearing a baseball style cap with the sponsors name, though there is nothing remotely related to baseball style caps and cycling.
Most cyclists who ride a lot don't wear a baseball cap on a bike, the large duck bill visor of this cap would just create more wind interference if tipped up or down and doesn't fit very well under a helmet.
On the other hand, the traditional cotton twill bicycle cap is made for what it is best at. Wearing while riding a bike. With it's short visor there is less wind resistance. Cotton twill is lightweight and while not an ideal fabric as it tends to absorb moisture like wearing a T-shirt, it still works well under a helmet for a layer of insulation. Plus it's a go anywhere item and folds up nicely in a jersey or other pocket
How did the professional bike racing realm change from traditional cycling caps to baseball caps as part of the team "kits" and on the podium? It seems influenced by the automotive racing realm, somewhat ironically. Or the baseball cap displays sponsor logos better on the front.
While there is always emphasis on the new and the high tech in the sports realm as far as clothing with synthetic fabrics, the traditional bicycle cotton twill cap is, and will always remain, a classic.
