They do! There's a few companies (SCRAP, PanIQ, The Escape Game) in SF already that are set up that way. They have a ton of locations, and host games for 1.5-2 years, and then swap them with other locations around the world. SCRAP also has some deals with media companies to do touring escape rooms; I've played a Zelda one and a Pacific Rim one.
There's also many companies that sell escape room plans. So rather than creating your own, you'd spend $5-10k to "buy" one and then build it yourself. They usually guarantee a X-mile radius that you'll be unique, so that you aren't competing against the same game.
Could escape rooms go on tour like theatrical productions? Producers swap escape room teams/spaces between cities? Professional roadies who are expert in setup/teardown?