Good grief, Keaton could barely move in that heavy rubber suit. He couldn't turn his head at all. Literally the first thing he did in his first action scene as Batman was to get shot and fall down. It was kind of pathetic.
What made West's Batman work, though, was that he wasn't goofy. He existed in a goofy world that he reacted to with absolute hyperseriousness. It was the same kind of humor that Airplane! used a decade or so later, casting actors known for their serious dramatic chops and having them play the most absurd dialogue and situations as if it were desperately intense drama. The reason West was so good as a "comedy" Batman was because of his talent as a serious leading man. He made it work by playing it straight, so exaggeratedly straight that it became comical.
Indeed, that's the biggest difference between B66 and the Batman comics of the late '40s and early '50s. In the comics, Batman and Robin were much more playful and traded constant joking banter as they fought crime. Robin was a nonstop wisecracker and punster in the vein of Spider-Man a couple of decades later, whereas the closest Burt Ward's Robin came to that was his incessant "Holy relevant reference, Batman!" schtick -- which Ward usually played hyper-seriously, rather than as a joke.
You could say much the same about Grant Gustin's Barry. He's different from Miller's, but still closer in personality to Wally than the classic Barry of the comics. Even John Wesley Shipp's 1990 Barry Allen borrowed elements from Wally, like the need for tons of food to fuel his speed and the affiliation with STAR Labs and Tina McGee.
Adapted versions of hero identities that have been shared by multiple people often amalgamate elements from two or more of them. For instance, Batman: The Animated Series's Dick Grayson wore Tim Drake's original costume and had his computer skills, while the sequel series's Tim Drake was closer in backstory to Jason Todd, and Superman: TAS's Kyle Rayner was given Hal Jordan's Green Lantern origin and costume. The MCU Peter Parker borrows elements from Miles Morales, notably his friendship with Ned Leeds paralleling Miles and Ganke Lee.
