I've never liked Boucher as a coach so my judgment might be unfair, but I still find it baffling that he was hired in the first place. It just doesn't make much sense to me considering the circumstances.
Dorion must have known that he'd have to manage this team on a strict budget for years to come. He doubtlessly also knows that his strength and that of management in general is identifying young talent. Additionally he should be aware of some general principles, like that owing to the way the RFA and UFA system works, you generally get the best performance-to-cost ratio from young players on their ELC or their first RFA contract. Furthermore, you would assume that younger players are on average speedier and have more energy than more established players, if for no other reason than from not having had a few minor or major injuries that have left their toll on the body. Not the least, it's been obvious for years that the NHL in general trends towards more speed and skill.
The obvious conclusion from all this would be building a team around speed and forecheck where young players fill depth roles in their first two or three seasons and then get more important roles to replace more established players (who the team can't afford anymore) for another few years before either becoming part of the core or being replaced themselves, thus perpetually rejuvenating your roster with cheap young players. This is even more obvious considering there was already a core of Karlsson, Hoffman and Stone of whom two are very fast and two are very smart players.
Instead he signs a coach that relies exclusively and stubbornly on a defensive, mostly reactionary, passive system and who has an above-average aversion to playing younger players and prospects even compared to your usual NHL coach.
As much as I dislike Boucher, ultimately the situation the Sens are in is mostly at the hands of management and ownership. Coaches and players have changed a lot over the past few years, whereas management hasn't. Dorion's job ain't easy considering the budget, but the roster has been and continues to be fundamentally flawed and he has made things worse by how he tried to fix them. He's now managed the Sens into a situation where he can either continue patching along as the goes, without any hope of turning this core into a real contender, or try to rebuild while already having traded crucial picks. I don't see how anyone can blame fans for seeing little hope for the foreseeable future.