Intermissions weren't for the patrons, they were for the projectionists. In the earlier days of cinema a single reel didn't hold 2+ hours of film, it only held about 15 minutes or less of material. Gone With the Wind, for example, came on 13 reels. A movie showing would require many reel changes, and switching between projectors. Some of the work for reel switches can be prepped ahead of time in the projection booth, but this takes space and time. Imagine how hectic it would be to switch projectors, take down the previous reel from the old projector, then prep it with the next reel, then do what you can to get the old reel put away and maybe prep the following reel so it's ready to go on ASAP. All of which has to be done in only 10-15 minutes time.

Now add in news reels, serials, comedy, and cartoons that would run before the main film, yet more projectionist work. Having an intermission meant that the projectionists could catch up on all of this work. It didn't hurt that it gave the patrons a break in what might be a several hours long experience otherwise (think about the 4hr long Gone With the Wind plus all the extra time from pre-film material).

A couple things made intermissions obsolete. The first was the invention of the "platter" in the 1960s. Platters are 4-5 feet across and are used to play entire multi-reel films that have been spliced together through a single projector without a break. This meant a single projector and a single projectionist could play an entire film (including previews) without having to take a break, or, indeed, show films in multiple theaters, provided the start times were sufficiently staggered. This gave rise to multiplexes since the labor demands for showing a movie were suddenly far less than they had been. It also highly incentivized the more modern experience of having a movie and all its associated extra material (shorts, previews, etc.) being packaged together in one neat bundle. In the multi-projector multi-reel era it was a trivial matter to insert extra material into the experience, just toss another reel into the mix. In the platter era the system was highly optimized for a "monolithic" viewing experience. With television providing a source for news, comedy, shorts, and serial format entertainment there was also less need and demand for that sort of content in the theater.

With the advent of the platter (and later digital projection) intermissions became something that was not both a benefit to the theater workers and to the moviegoers at the same time. It became a cost to the theaters because it translated directly to fewer film showings per day. That can actually have a non-linear impact on revenue because there's a fairly narrow window of time where people primarily watch movies in the late afternoon and evening, which only allows for maybe 2 or 3 "prime time" showings of a film in a single auditorium per day, reducing that from 2-3 down to 1-2 translates to a lot of lost revenue, potentially much more than might be made up by extra sales of snacks and beverages.

Additionally, intermissions in a multiplex are a different beast than intermissions in a single auditorium theater. In a multiplex you now have more opportunities for people to sneak from one movie to another (not just at the intermission, but at the beginning) simply because there are more periods of time when there are crowds in the hallways. I don't think there's any data out there on how much that contributed to choosing to abandon intermissions, but it was at least one contributing factor.