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:
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. It's just the same way you can't say わざわざ来てください. In fact it may be appropriate to think of やってくる as わざわざ来る, expressing some amount of deference toward the subject, making a command feel unnatural. I can't find any instances on google of it being used as a command. It's like in English you wouldn't issue the command to someone, "Go to the trouble of coming here."
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。