The dictionary is unfortunately vague on this matter, but some discussion elsewhere on the web lends some clues to the nuance. These discussions say that やってくる, as you suggest, places more emphasis on the act of coming, but especially that the traveler came with some particular effort or purpose, or from especially far away.
From the second link:
「やって来る」は「苦労して、はるばる、遠くから来る」と言うニュアンスを持っているのではと思います。
The writer goes on to list a few examples. If this is the case I think it seems clear why you wouldn't say やってきて to your friend. It almost has kind of an お疲れ様 kind of feel to it. I can't put that exactly into words. Maybe that it just doesn't fit well to give a command with a verb that has that kind of nuance to it, or maybe we can think of it purely as a descriptive word rather than as a command. I can't find any instances on google of it being used as a command. In terms of overlap I just think of やってくる as a more descriptive 来る that can't be used as a command.
There's also the meaning wherein you can use やってくる to refer to work you've been doing for a long time, like もう２０年この仕事をやってきた。