Supergirl and Legends of Tomorrow 2018 schedule

I don't know, it kind of worked well enough, in my opinion, when Agents of Shield did that with Peggy Carter; with the latter airing during the formers break. Logistically, I think it makes some sense to coordinate things so as to minimize the amount of down time between new episode; since so often people are put off by reruns and some are even surprised, as if it were something new, when it happens every single year. At least in this case, as with the aforementioned SHIELD shows, they're filling in those breaks with content from the same general source, rather than airing something completely unrelated. That might not mean much for viewers who don't watch all of the Arrowverse shows, but there's potential there to use that to their advantage, and make the stories work in concert with one another.

Many years back, I pondered how the vast array of characters and stories could be brought to the small screen in a practical way; and the idea that I had was to do a two hour block with rotating segments, ranging from standalone episodes featuring the likes of Batman or Superman, which would invariably recur on a more regular basis; or have the occasional one offs for (then) lesser known characters, like Green Arrow or the Atom. And this format could be a mix and match, with shorter or longer episodes paired together during that block, or the occasional feature length event for crossover.
I never dreamed of seeing a time where a network would commit to 4+ live action superhero shows airing at the same, sharing the same universe; and spread out across multiple nights of the week. So from that perspective, dovetailing the programming in such a way as to have two of the shows share a timeslot for some period of their season and allow for a continuous stream of content doesn't seem too outlandish. The real challenge is, as always, the writing; and whether or not "Legends" is up to task is, as ever, up for debate...

What I think could be good, and it probably won't play out this way, but if they known about the scheduling shift ahead of time (which, for all we know, they might have) and worked it into the story - like at the end of the last Supergirl episode leading into the break it appears Supergirl has died; and for the next nine weeks all of the other shows learn of this and mourn her. Then when the show comes back they do a "Supergirl Lives" story, with her coming back thanks to the fortress and probably Superman's help.