> I figured someone who speaks X and wants to begin learning English would use an X-English / English-X dictionary.

At first. You should switch to X-X dictionary as soon as you can, far before it becomes natural and easy to use X-X dictionary. X-English/English-X dictionaries encourage people to continue "thinking" in their language, while successfully learning a new language would absolutely require embracing new ways of forming phrases, building sentences, etc.

Source: English is my 3rd language, I'm on my 5th now.

Two things have improved my English more than anything: deciding to read out loud whenever I'm alone reading an English text, and discovering that I can immediately look up any English word with a three finger tap on OS X.

If the dictionary had been English–Swedish, I think I would have been more prone to see English as an obstacle, as something that I need to translate to Swedish in order to comprehend the text. Instead, I constantly find myself thinking in English whenever I read or write English, which I never did before.