Reasons why theatre has intervals and cinema doesn't:
Theatre is *generally* longer than cinema. Hamlet is over four hours. Many, many plays are 2.5hrs and more, whereas that's a minority and exception an cinema.
Plays are written in acts. Usually five or three (the interval generally comes after act 3 or 2, respectively), but occasionally a nice neat two acts. But structured in acts which are clear chunks of story, designed to stop the action. They are also written with the knowledge that there will be a break. Many plays build in a cliff-hanger for the end of the first half, using the interval to enhance the storytelling and atmosphere. It's a bit like when albums used to be put together so as to end the first side with a really good track. You would need to write this into films. You can't reliably reverse-engineer those moments.
You only get eight performances a week into a theatre. A cinema can easily do four screenings a day, per screen, seven days a week. The actors won't get tired. Therefore, theatre must all-but-compel its fewer patrons to buy stuff. The "interval drinks" ordering system is especially clever.
Audience nipping out for a wee at the cinema might miss stuff and distract the audience... But if they do it at the theatre, they'll miss stuff, distract the audience AND potentially distract the actors.
But then, also, the trend in theatre is to do away with the interval anyway. I've been to two or three plays in the last few years at the Young Vic alone, which have done away with the interval, preferring to take the audience on a single ride to the end. Artistically, theatrically, intervals are a bit of a PITA.
