I think that you are answering your own question there, Jake.
If it was 100% evident that he was effective both offensively and defensively, then what reason would he not be on the first or second line 100% of the time? Wasn't a part of Chayka's philosophy that there was a clear message throughout the organization, from GM to coach to scouts to trainers regarding what needs to get done? If they are following that line of thinking, then it is not solely on Tocchet's shoulders, but also on the GM, and others as well.
You're scraping for answers when everything in the way that our management team had been shooting for suggests that this wasn't a one-off scenario where the coach goes off-script from every other piece of information in other areas. This was evident to the GM that there was a lack of something on Strome's part, as well as the coaches, as well as strength/conditioning, and even so far as to be noticeable to the other players on the team.
But again, you want to put every ounce of blame on the coaching staff alone, and treat Strome as if though he was absolved of any negative attributes to his play. It sounds like you have never had the opportunity to coach any sport on any level and fail to understand that if someone doesn't show the ability to get some parts of the process done, then it is common place for a coaching staff to ignore where a player needs to get better at for the sake of just getting him minutes.