I agree and I dont think Koeman particularly had an issue with it, I just dont think Walsh was strong enough to deal with him
The fact they both joined the club at the same time led to the strange dynamic. Walsh was learning about the club, his new role and what was expected of him and Koeman's strength of personality and obvious backing from Moshiri wouldn't have led to a straightforward relationship. I can well see him acquiescing to Koeman during this period.
In my opinion Walsh will probably be wiser in the role now, will have had his authority respected with this managerial change and we should now see more of a better balance with the new manager. I think his role is vital really and it'd be silly to even think of changing him in the near future.