Being a native Russian speaker and a linguist/polyglot I have always been fascinated by fake Russian accents in Hollywood movies. My question was always why would you cast a Serbian, Bulgarian or some other actor of Southern Slavic descent when you can find plenty of Russian speaking actors. I guess because Southern Slavic, Hungarian, Romanian accents sound so distinct they became a stereotypical accent in Hollywood movies. If you want to hear how a real Russian person would sound then listen to Armie Hammer in Man from UNCLE, he perfected it, it was so spot on.
Back to your question. Because actors say what's in the screenplay which is usually written by native English speakers, they just memorize it. And because directors/writers are not linguists they don't bother thinking of such small things like a discrepancy between harsh accents and grammar, which logically should be somewhat on par with each other, to make it more realistic. And nobody really notices it or complains about it. There are of course people who have strong accents, and have perfect grammar, yet in majority of cases a strong accent usually implies bad grammar, but as your grammar improves so does your accent not because there is a correlation between the two, it's because you practice more. Of course this not true for all movies.
Now if a director wanted to incorporate both bad grammar and a heavy accent, it can easily be done without sacrificing intellgibility e.g. I come tomorrow to killing you or You watching your back from now. It would probably make it even more entertaining. Characters with heavy accents usually speak in short sentences and don't go into long philosophical discourses.