I would love to know the ages of those people, also if they're hardcore Batman fans or just fans of the movies.
I can see this though (most are in their 30s or late 20s, some older) because really Adam West IS Batman. Bale is famous for so much more than Batman, and would likely be famous even if he had never played Batman. Keaton was also popular from
Beetlejuice before he played Batman. With Adam West he became that role and that role became him. When Adam West plays himself in
Family Guy or is depicted on TV, he's always depicted in his Batman character. He even shot a pilot with Conan that yutzed on him for playing a detective in his early acting career. Adam West's career starts and stops with Batman, and most of the time Batman gets recast there is some reference to West.
I remember when Bale was cast they said it was the first time an actor over six feet played Batman since Adam West, citing Adam West's height as the "actual height of Batman" (6'2").
Also a lot of people, even ones who weren't alive were first exposed to Batman through Adam West. I watched those long before I'd even heard of BTAS, Keaton or (of course) Christian Bale.
Plus, as I say Batman the 1960s show contributed an awful lot to the fiction, so it constantly gets referenced, especially being the first major hit for the character.
Plus the some "Batman! nah nah nah nahnahnahnahnah Batman!" is one of those songs everybody remembers. Then the car is iconic, shows up all over the place. A lot of fans may hate the "camp", but it was very popular, and it's one of those things once you see it just sticks in your mind.