I truly believe that it should happen.
I think that it is the dream every MCU or DCEU lover thinks impossible, but is wishing so hard to make it happen that it could actually be true. There is no such thing in life as two big "different" universes meeting each other after years living with each other. We've all saw different crossovers. When I am saying that, I am thinking of Arrow vs. Flash, Nick Fury and Black Widow in Iron Man 3 (which had to happen to make The Avengers, just sayin'), there are a whole bunch of other examples out there, but I am not here to talk about the multiple crossovers that happened, but to make a point. If they made all of those crossovers, why not making a big crossover of the two universes? Maybe the two companies cannot work together... We have no idea. In fact, what I am saying here, right now, is just suppositions over suppositions and hoping that someone highly placed in the film industry would read it and decide to make this big idea a reality. I know, I am not the first one to come up with such an idea, I even read another post about that before righting this whole thing. I am just trying to show you that it would be possible, and that it would be (for me) a great movie. Talking of money, I am sure that it would be a great lucrative film. And if you are not sure, head to google.com and search "DCU vs MCU", just for fun. You should get a LOT of websites talking about it like it will happen next year and that the first critics are already out and SOOOOOOOO positive (which never happen, there is always one person who didn't like the movie).
Now, let's think about it for a second. This is not a dumb idea, at all. The simplest idea, even if the movie is the worst ever, will make the production a LOT of money. Actually, it would probably be the most lucrative film in history, or at least the most lucrative about superheroes. From that part, we will be thinking about it as if we were fans (which I think we all are, deep inside) Imagine: The Flash arrives to Gotham, because he was taken there. (the reason to be revealed during the film) He escapes from the place he is locked in and meets Batman. They have a fight, for some reason, and they finally decide to team up to fight against a villain (Find one by yourself!) then, they call their respective associations to ask for help, they are not enthusiastic about the idea of working with another association, but they finally accept and they fight against the worst both DCU & MCU villains. Would be a 2 parts film, though. Just sayin'! With that being said, if you was not convinced that it could be a good idea, I hope you are now.