I'm guessing, and like many others have already pointed out, the system could be made small. Engineers have pretty much always been troubled by the limited amount of space to hold each and every system in a fighter jet.
Using air will impact performance. It requires piping (which again occupy space and adds to weight) and it would need to steal air from the engine, which could otherwise be used for more thrust.
Engines back when the MiG-21 was still relatively new and shiny wasn't very efficient on the "air" part (and still aren't, since engines for fighters are generally developed with power in mind).