Regarding kessel as a potential problem going forward, there's probably some logic in the belief he might convert a few more of those hit posts, flubbed shots, and missed empty-nets in the future if he's a bit luckier than he has been thus far. Managing to find himself in those situations to begin with is a good sign that with his history of goal scoring he could in theory convert on those at a better rate at some point.
I personally couldn't care less about his perceived softness along the boards or in corners, this team hasn't had a grind *****es down mentality in a long while, and even when they did sykora still found a way to contribute adequately. Speaking of softness, pay close attention to ovechkin from time to time, specifically how long he actually carries the puck or holds it along the boards before either passing or shooting, it's not very long. His physical reputation comes from his propensity to level unsuspecting opponents who don't see him coming, otherwise he avoids physical punishments as much as any other player. This undoubtedly contributes to his ability to stay healthy comparatively to a crosby or malkin, who because of being center's and driving the play for their lines take far more unavoidable physical abuse simply from fending off defenders as they're carrying the puck around the ice trying to find lanes to distribute it to their wingers.
Ovechkin being the finisher on his line is the intended destination of the play, not the source, and thus isn't put into position to absorb hits that he's not prepared for all that often. Kessel is similar in this way, he stays as healthy as he does because he avoids unecessary risk, thus even though he is a good playmaking winger, he shouldn't be the one dictating the play for his line all that often outside of off the rush chances, as he's not going to body off a defender to maintain control of the puck or be the one digging in corners to maintain possession. As such they need to play him with linemates who can and excel at it to make up for that.
This is where my only real concern with him originates from, which is his complete inability to one-time a shot or wield anything resembling a hard slap shot. The way this team has operated for years is running plays through crosby and malkin and needing the recipients of their passes to be able to quickly convert on the chances they're given from the defense focusing on the center's. Kunitz before he slowed down and especially Neal excelled at this with their quick and accurate releases. With kessel thus far he's been wholly incompetent at quickly getting rid of the puck once given it in high scoring chance areas because of his inability to cleanly shoot the puck without first corralling it, which wastes precious seconds where the goalie or defense can get in position to stop it.
Whether it's because of his stick or refusal to adapt to a new play style, that aspect of his game might not get better in the future. Which means if they're going to get as much value out of him as they hoped, their offensive philosophy as a team, specifically that of crosby and malkin might need to be the things that change to adapt to him. If that's not feasible or acceptable, I see no issue with believing he's a bad fit here and his cap could be better spent elsewhere, which has nothing to do with feeling he's lazy, fat, etc. They're far past the point of being good enough to compensate for hurt feelings, scuderi was the first step in the right direction, kunitz should be the next, and if kessel ends up requiring the same treatment at some point, so be it.