I think it's helpful to have a complete understanding of what the GM does, beyond signing players and hiring coaches.
The Calgary Flames website gives a brief job description:
In his position with Calgary, Treliving reports directly to President of Hockey Operations Brian Burke. He is responsible for all team personnel decisions, both players and staff; manage the amateur and pro scouting staffs; as well as other administrative duties required of the general manager. He is also responsible for all player personnel assignments with Flames’ minor league affiliates.
That's a lot of administrative duties. Think of all the time that he must spend in scouting, recruiting, negotiating, and managing every single player AND staff person on the payroll of the organization. It's a lot more than a nine-to-five type of job; he probably shows up earlier and leaves later than anyone else in the arena, just to keep his head above water.
Just to provide a sense of what GMs go through in order to prove themselves at a lower level and actually be qualified for an NHL position, here's an actual job description from a women's pro league:
Communication
- ensures conflicts and concerns between players, coaches,
and managerial staff is addressed.
- Communication between the league and team, meaning the General Manager must act as the main point of contact for all matters and transactions
- Communication between team and association, in cases where the Team is affiliated with a girl’s hockey association
Team Selection
- recruitment and selection of all team personnel
- Coaches should be selected by a committee within the team personnel that is then mediated by the General Manager.
- ensure that all rules & regulations that govern the recruitment of players will be followed as to the CWHLs policies.
- recruit and select staff members such as Equipment Manager
and Team Trainers.
- recruit and train Game Ticket Sellers, Time Keepers, Announcers and so forth including both game day staff and event promotion.
Team Rules
- CWHL Code of Conduct must be ensured by the General Manager
- The General Manager must develop a team Code of Conduct
Team Eligibility
- being aware of special conditions within eligibility is crucial such as substitute goaltenders, USA/International player transfers/tryout etc.
- Roster submission to the OWHA and CWHL and reporting of all Roster changes to the OWHA and CWHL.
Team Records
- The General Manager must ensure that the team records are adequately maintained.
- This information should consist of roster list, contact lists, medical information, schedules, game reports, and financials.
Team Financials
- The General Manager is responsible for their team’s finances and must ensure that they adhere to all of the policies and procedures of the CWHL this includes budget development and financial records.
- The General Manager is responsible for ensuring that their teams practice and game ice is confirmed and booked
Game Day Operations
- The General Manager is responsible for ensuring that the games run smoothly and the necessary protocols are followed.
Travel Organization
- The General Manager must coordinate all travel arrangements through CWHL-approved service providers.
Media & Marketing
- The General Manager will serve as the point of contact for media and marketing- related issues surrounding the team. Media and marketing includes the General Managers responsibility to promotion of games and community involvement that their team
participate in locally.
Fundamentally, the expectations of an NHL GM are the same as in this lower league. Of course the stakes are MUCH higher in the NHL, the issues are MUCH more complicated, and the staff and resources available to the manager are MUCH greater. So he has to have the organizational knowhow to put together a staff that can make all of these things run properly, then delegate responsibilities and manage the staff as necessary.
There was a good Hockey Writers article a couple of years ago that described the specific skillset that's required to do that job successfully:
http://thehockeywriters.com/overtime/winning-nhl-general-managers/
Now... imagine doing that AND coaching the team at the same time. Not gonna happen. GM'ing is a hell of a job unto itself.