Studios did use to own theaters back in the old days. Paramount especially used this to their advantage by owning multiple theaters, utilizing block booking, and holding exclusivity on what theaters own. Basically imagine if Disney owned AMC Theaters, then AMC would either play nothing but Disney and Fox movies, or movies from other studios would get the short end of the stick in terms of showtimes and exhibition. But in the late 40s, the US government banned the process due to it violating antitrust laws.
Having said all that, the Trump administration did mention they were interested in removing these laws, considering them "outdated", though I don't think that went anywhere. Maybe it will, maybe it won't. I don't know how Amazon works since despite having their own production studio, that's not their #1 business.