Heck, look at the first FLASH tv series back in the nineties. That show debuted years after "Crisis on Infinite Earths," but it's not like the TV had to bog itself down with lots of complicated backstory involving Jay Garrick, Wally West, the heroic death of Barry Allen, etc. They just stuck to the basic premise of a guy in a red costume who is The Fastest Man on Earth.
Nobody cared if it was "pre-Crisis" or "post-Crisis" Flash . . .
Right -- and they gave Barry elements of Wally's character, like Tina McGee as a colleague/love interest and a need to eat heavily and frequently to feed his metabolism.
Not to mention all the Marvel movies that have blended elements from the classic and Ultimate universes, the animated series that have drawn on elements from different decades, etc.
Batman: The Animated Series, for instance, was an amalgam of concepts, characters, and storylines from the '70s through the '90s, both pre- and post-Crisis (and occasionally the '60s with the reimagining of characters like Mr. Freeze and Clayface), plus the occasional element drawn from the Burton movies, and plenty of its own original ideas.