I'm pretty sure the main reason was to better leverage their future streaming service because while they most likely will sill release Searchlight and 20th Century movies, there's only so many movie you can put in theater in a year. They have to fit Disney Animation, Pixar, Disney live action, Marvel, LucasArt, 20th Century Fox and Searchlight in a calender year. Knowing that Fox is releasing about the same amount a movie a year than Disney, some stuff are going to get thrown out.
I personally don't expect streaming to salvage most of that.
That leverage is true, yes, but I wouldn't say that owning previous films made by Fox is an ultimate seller here, the studios themselves have such a pedigree and Searchlight are a fantastic house for either picking up, distributing or making films.
I disagree, however, on your assertion about 'so many movies', there is no reason for Fox or Disney to release less movies. Films like The Favourite, Grand Budapest Hotel or Brooklyn don't exactly suffer from Star Wars or the thirtieth Marvel movie. Sure, there may be crossover (there likely is) but I don't expect Fox or Marvel to worry that much.
Case in point, Lucasfilm released Solo less than a month after Infinity War. There were massive slates in November and December that Solo could have stood in on its own and not go against the largest franchise in cinema, hell, they're both Disney.
So I'm not sure it'll work out like that.
