Why didn't silent movies have subtitles?

Film was exposed only once and the quality was not good enough to film the projection of a movie in order to add subtitles underneath in a copy. The only editing tool was cutting and that's why movies had intertitles (text cards) between shots.

As a note, George Méliès, among others, did experiment with multiple exposures but it made parts of the movie blurry and was only useful for adding ghosts or for dream sequences.

You're right about the cost. As recently as 1970, subtitles were expensive. Eg polish budget film Hydrozagadka had an actress recite credits instead of displaying text - just because it was cheaper.

Our mindset is spoiled by computers applying subtitles effortlessly, but in film times it was huge work. Even when the technology was perfected it was expensive. (And as others answered - in silent movies the technology was at early experimental stage.)

Intertitles were never called "intertitles" during the silent era. They were just "titles". We call them intertitles now to distinguish them from subtitles and the main titles of a film.

Subtitles were used occationally, like in Clarence Brown's FLESH AND THE DEVIL (1926), when John Gilbert hears Garbo's character name "Felicitas" over and over.

The main reason that they were not used, is that silent films were translated into many languages and exported all over the world. It would have been a lot of work to superimpose subtitles of different languages over a changing scene. The translations were usually done in the country where they were shown, not at the studio in the producing country. This also came in handy when the movie bombed at the box-office, or was reissued. It was fairly easy to cut in new dialog or intertitles to change the film.

The purpose of subtitles is to generally allow audience members to mentally pretend that the words they're hearing are actually in their own language. In most cases, the purpose of intertitles is to allow the audience to pretend that they can hear things that they see the actors saying. In order for the latter mental substitution to work, however, the audience needs to be able to actually watch the actors, which means they can't be trying to read the text at the same time.

Using subtitles would have been a technical annoyance but not an insurmountable one, especially if one was willing to reserve space on the screen for them. Multiple-exposure photography was not difficult, and if one were using interpositives one could produce an internegative with subtitltes in different languages without requiring extra steps in the final printing. Handling multiple languages while using direct printing off camera negatives would have required more complicated printing steps, but nothing insurmountable.

I think the much bigger issue is that even if subtitles had posed zero extra technical difficulty, intertitles would still generally work better for dramatic purposes in silent films.

It seems to me that, in addition to the various other reasons mentioned, that even if it were a viable option to use subtitles, they might not have been preferred to intertitles for silent films, because they require the audience to choose whether to read or to watch the action. When silent films were current, the moving images were a spectacle, and people may not have preferred having to read the words during the action. Even for audiences used to subtitles, they distract some attention from watching the action. Intertitles also facilitate the style used (of acting and writing) where the words shown are not literally everything that would be said, which works well when sound isn't used.

Edit: As TheBlackBenzKid commented about the reasons why keeping watching the image was particularly important in silent films:

"I would further add to this opinion that is also based on art and body language. The music and the sound played a big part as well as actor facial expressions etc." – TheBlackBenzKid

Also films were made for an international audience. Intertitles could be cut out and new ones put in for each language.

I suspect that part of it was that, for an artistic standpoint, lack of dialogue was just part of the medium and they were all about action and gesture and writing a dialogue script wasn't part of the process.

Even with modern sound films the decision between dubbing and subtitles for foreign language sis difficult and both have pros and cons. A particular issue is that with a primarily visual medium subtitles are a massive distraction.

In fact even with traditional theatre and even opera you get a similar effect. With something like Shakespeare a lot of the writing is about rhythm pacing and putting a hard emphasis on key lines. Traditional theatre acting tends to be quite stylised simply because it is hard to make out every word and nuance from the back row.

So actors and directors were sort of used to the idea that everything had to be big and emphatic.