Do most people have more than one theater that they visit frequently? I'd personally be fine with a subscription to just one chain, since almost all chains have almost all of the content.
Well, there are standard theaters that have the blockbusters, and you are right that the chain really doesn't matter, but there are also art theaters that have the more intellectual films not shown in the big theaters. Those generally aren't owned by chains. Currently MoviePass works with both the chains and the indies in my area. Which is great for as long as it lasts.
I only have 3 chains near me, but I visit different ones based on schedule. Theaters are a commodity to me, except for a few drafthouses that play special movies.