The answer to this question depends on a number of things - very few of which ANY of us here know the answer to:
1) Is he happy just remaining a coach, without serious ambition to be a manager (nothing wrong with this if so)
2) Is he a good coach (NB not manager)? (No one here knows an answer to this question, but from what bits we do hear, it would seem that he is.
3) Did Frank Lampard Lampard want him on his coaching staff, independent of any other influence (obviously related to #2)
If the answers to these questions are yes, then I'm delighted he stayed on, and it was absolutely the right thing to do. If there's a couple of no's in there, then he should have left.
There is of course the additional possibility that the answer to (at least) #1 and/or #3 is no, but he's remaining in-role temporarily to assist the handover and while looking for other roles outside the club, which I'd have no particular problem with.