(IMHO) I don't see anything wrong with emulating someone else's style if we find their style of playing appealing. That is how one develops their own style. There has to be a frame of reference and influence in order to start somewhere.
Every great guitar played cites certain influences. As one example Chet cites Merle Travis, as do many others. Doc is the unofficial defacto standard when it comes to flatpicking, and countless players from two or three generations have been influenced by him.
You build up chops by listening to other players. You copy their licks and riffs. Why? Because they sound cool to you and you want to do it too. The trick is in taking these arsenal of chops and licks, patterns, etc....and re-arranging them, distorting them, simplifying them, or adding more complex things to them.....and then, you have your own style.
I agree with you that no one can sound like Doc but no one's gonna leave the room if you start playing like him, at least anyone with any taste.