Unfortunately, this is prevalent in all types of businesses today. Senior leadership in almost every organization is focused on the next quarter. In hockey the GM is only focused on the next season, or at the most the next three seasons. Why? Because as you have correctly stated the GM is not going to stick around to have to clean up the mess.
Imagine being a fan of the Sabres. Sure you're excited to get to watch Skinner for the next few seasons, but for that privilege you have to watch him decline the last 3-4 years of his contract. That type of situation doesn't inspire me to buy tickets to any games, much less season tickets. Winning a Stanley Cup is very difficult. I don't expect the Kings to ever win another one in my lifetime, but I do expect them to have a plan to get there and try to execute on it.
I may not be the typical fan who may be satisfied going to games and swooning over one or two stars on a team, or getting wrapped up in fond memories of long past glory. I think the owners are obviously using the wrong metrics to judge their employees, but I could be wrong. It is only going to change when there are a lot of empty seats at various arenas with several late-30 somethings skating for both teams.
I notice in the news there are a lot of teams in MLB this season with almost empty stadiums, because the owners don't know how to put a competitive team on the field, or even show their fans they are building something. I hope the NHL owners figure this out and get rid of the guaranteed contracts, so there is a constant flow of new and better talent into the league. That is what this fan wants, and the fans pay the bills.