Having good people
One of a GM's primary responsibilities is to build a successful team. That may entail some time solving task-oriented problems, but the majority of problems he/she has to solve are people related. Surround yourself with good people who are smarter than you (or, at least, they should think they are). Develop a good understanding of your key people and what motivates them.
Being a team leader
If you approach general management using the metaphor of managing, coaching, directing a team, you will not be lonely since you have to be intimately involved with the team members. If you are humble enough, you can always get good advice.
Bench strength is important. Cross train your people so you aren't left in the cold if something happens to a key player. People like to be challenged in new tasks and it makes the company more flexible.
Cross training is key to a CEO's success. Sometimes, I would find myself training a new kitchen manager, while at other times I am debugging my CFO's spreadsheet. The most important thing, however, is not to fall in the trap where, because of your own proficiencies, you end up doing a subordinate's job.
Our job as general managers is to bring people along and make sure we have the best people for their jobs. But we must resist the temptation to do their job, lest our own job of leading and setting the vision remain undone.
Facilitating effective teamwork
For the GM, having a good team is an absolute win. But it is important to keep in mind that even one level down, it's not always that clear that teamwork is a win-win for the participants as they see it.
I can't count the number of times that I have been able to get my team functioning with me as the leader, only to see the team members under-communicate, avoid one another, and generally fail to work together without me. In retrospect, it is easy to see why, because they don't necessarily believe that they will get recognition if they are not performing in front of my eyes.
That's why I always try to place a very high value on the concept of teamwork and am fairly direct in my criticisms when I note that a problem failed to be properly addressed or to be resolved because the individual failed to generate effective teamwork among his/her peers. For me this is a major error signal! As a GM, you really need to have good teamwork happening when you are not around. Making it a value requires a great deal of persistence and reward and punishment...all carefully manipulated.
Hiring the right people has always been the top priority with me and therefore also with my functional managers. In some cases we have left critical jobs open for as long as a year because we could not find the right candidate to fill it. This has always paid-off in the long run, though it makes life very difficult while you are covering for the missing person (usually a team effort) and aggressively trying to hire (an added task to an already full day).
The one time I broke this rule and hired someone that was "good enough" for a position we need to fill quickly, I paid dearly through six months of trying to make it work before removing the individual and then starting the job search all over again.
Training your replacement
In regard to one's reluctance to develop line managers for fear of being replaced by them, I offer this advice. In my experience, a GM cannot survive without top-notch line managers. I firmly believe that if you are successful in developing your line managers to one day replace you, then chances are very good they will still be reporting to you or several levels under you because of your success in developing people. If your company does not view it that way, there are a thousand others out there that do.
Someone wise once said, "The harder I work the luckier I get." Luck figures into everything we all do. But if you apply your creativity and energy to generate, identify, and exploit opportunities, eventually you will stumble onto a good one. Maybe the person who does all that is "lucky" -- but the person who isn't out there trying things won't ever even have the chance to be "lucky". A key role of a general manager is to encourage everyone on the team to think about new opportunities and the best way of taking advantage of them.
A successful leader will be able to optimize the performance and potential of his team irrespective of the range of skill sets, abilities, motivation/enthusiasm/morale levels, degrees of dedication and loyalty, and personal and professional priorities of the team members. No team or individual team member will ever be perfectly suited for the task at hand.