DC's mistake then was trying to combine practically all of their multiverses into one
It was necessary for the company to survive publishing going forward; until the brilliant answer provided by Wolfman's COIE, DC was seriously hobbled by an unwieldy
mix and mess of some great runs (certain
titles from the early 40s, then the late 60s through the early 80s), but that was surrounded by
decades of silly, near worthless material, especially from the late Golden-to-early-Silver Age, with few exceptions. DC had to clean house and make sense out of too many self-created and acquired licenses, or fall apart. The answer was clear, and it was a spectacular, historic success, as fans were finally able to see a logical plane of events in the DC universe instead of the cartoonish, "name-this-week's-universe" approach for so much of the company's history.
The CW version would do well to follow that grand set-up, unless it does not matter, as most of these shows are not going to last long enough (in the grand scheme of things) to have that much content. That said, they could take the preemptive strike and merge a couple of worlds / kill a few characters just to establish that, even if the characters will rarely share screen time.