"Come in" is fine because "in" is being used as an adverb, not a preposition. You can say "He is in the room", but if there is motion toward something and the preposition is followed by an object, it has to be "into": "Let her into my life". "Let her in my life" is grammatically incorrect. The sentence "Don't come in the kitchen until I finish the cake" is not correct, although most people would probably say it that way as a shortcut. It should be "Don't come into the kitchen."
I think it's a mistake to start down the "correcting grammar" path to the extent we are doing it here. Most people when they are speaking, take shortcuts and don't speak the way they would write something.