Well, it does affect role-playing. And my assumption is that in certain political intrigue campaigns where "what faction are you from?" is a major question asked of the PCs all the time, the appearance of the Echo can be, at least occasionally, important.
What happens if you use Disguise Self? Does the Echo look like original you, or the you that is under effect of Disguise Self?
RAW - only the original you, as the echo is a fragment of you from a different timeline, not a copy of you now.
Okay. Slightly different question: If my PC is a Changeling, which of my potentially thousands of faces would the Echo Knight have?
Well, it does affect role-playing. And my assumption is that in certain political intrigue campaigns where "what faction are you from?" is a major question asked of the PCs all the time, the appearance of the Echo can be, at least occasionally, important.