That makes good sense. I expect Edward would be on board with that plan, if he were fully aware (which would preclude the need). Current circumstances are preventing it, and as Tedd is in Arthur's office, it makes sense for Arthur to be giving Tedd advice at the moment.
We don't know an awful lot about Arthur and Edward's relationship, but I get an impression that Edward has some personal issues with taking advice; he's apparently been burned by Adrian Raven, his mentor, and has expressed some negative opinions about Arthur. He was considered overqualified when he joined and was not primarily trained by the organization he's a part of, i.e. maybe not fully in tune with their philosophy. Maybe there's something going on like Liz, seen bad side of things and no longer has basic trust. If that's the case, I'm not sure who would be in a position to reach out to Edward and talk to him. Literally kicking his butt is not likely to work, which I'm sure you know.
We haven't seen him being emotionally close to any other adult. It seems like he built up many walls after Noriko left. He does seem protective of his former agents, but I don't see them as being in a position to give him this sort of advice.
I do get the impression that having figured this out, Arthur would at least mention it when it is convenient to do so. Arthur seems to have a more than adequate concern for Tedd.