Do they? No one wears helmets to play football, association or Rugby. Scrum caps maybe but that is to reduce abbraision not protect from impacts.
Also, scrum caps can only be 1cm thick and must not be black so that damage to helmet or wearer can be seen easily - rules on maximum size and damage-evident colours seem like they would be good additions to cycle helmet standards, reducing the risk of helmets increasing impact probability through unnecessary extra size and of subtly-damaged helmets being used.
Professional cyclists and motorcyclists generally don't have free choice: they are compelled to wear them on pain of disqualification and the pro's are often co-sponsored by helmet manufacturers, so it's pretty unlikely that they'll speak out against them while a current pro. As such, it's hard to say what their real views are, but a lot of cyclists have been spotted riding without helmets (there was
a controversy at last year's Giro when Contador rode without his for a bit, yet escaped punishment I think because only fans saw it, no referees) and many more wear them in a token manner, with loose dangly chinstraps or wild angles.
If you want to look at sports, then an interesting one is boxing, where head impacts are very common but use of headgear has become less popular recently.
But all this is mostly irrelevant. Cycling is an activity and not a sport for most people.
(edited to add link to a Contador incident)