What do you mean "do immediately after BvS"? Make a team? If so, the only one who would possibly join would be Wonder Woman. But it didn't make sense for her to do so, as she was just rejoining the world. I thought the her scene at the beginning did a good job of showing how she was starting to be a hero. Cyborg was still in the being created stage. Aquaman and Flash were in the "we know they exist but have to locate them" stage. So, Batman had the long vision to see that a team was needed, but didn't have the means to create it yet.

When it was possible to make a team, Wonder Woman and Flash were immediately on board. Aquaman and his negative attitude was not (which made sense to me). Cyborg was unsure, and since he was just learning how to live and every day something was different with his new body, that made sense to me also. Why should those two just immediately jump on board with some crazy guy in a bat suit?

I, too, hated pretty much everything about Doomsday from that movie.

The mother boxes were pretty much active from the time they joined. The world was starting it's transformation process. It seemed pretty fast to me.

That reminds me of another (small) complaint I had: if part of the world was turned into Apokolips, why would it still be safe after the Mother Boxes were separated. Why would it sprout flowers?

The Boom Tubes looked good, though.

I was hoping we'd see a glimpse of Big Barda, and maybe Darkseid and some of the Furies, or at least Granny. But nope.

It seemed like Granny Goodness was in Thor: Ragnarok.