A movie studio cannot own a theater and exclusively run their own movies. The Supreme Court decided this in United States v. Paramount Pictures, Inc., 334 US 131 (1948), a landmark anti-trust decision. This was a fascinating case because it led toward the dismantling of the "old" studio system, where a studio owned everything and everyone from pre-production through distribution. It also led to the explosion of independently-run theaters and gave smaller studios the room to get their movies distributed. It still is relevant today when companies such as Apple or Google or Microsoft are trying to make both devices and content. It could be that Disney buys up these theater chains, but they would need to run other studios' movies as well.
Its going to go the route of the collusion we see in cable companies with wink wink under the table deals. Which lead to higher prices.