Is it strictly the strategic or penal nature of the holes?
Perhaps, but the setting is also important. I can't think of too many great courses that don't have great natural sites with lots of drama. I think a great course is one that fits the site perfectly, but not at the expense of quality golf for better players. Torrey Pines falls short of greatness on a great site, because the golf was never as great as the views.
Should it include an ecomonic element, such as how often the locals (or members) play the course, again and again?
Not really. Some of the great courses don't make financial sense, but they are great anyway (as long as the last)
Should it include the ability to reasonably maintain the course, or if the maintenance overly burdens the course (financially, playability, requiring frequent changes, etc..)?
With money, you can maintain anything, so I would say no. It should focus on the architectural feeling.
Should it matter what else the architect has built? Does the course have to compliment or enhance the overall portfolio of the architect, or can it be the one-hit wonder in a portfolio?
No, then we would be considering a great architect, wouldn't we?
Should it take into consideration the types of events it could hold? (professional championships, amateur championships, member-guests, ladies 9 hole league, etc..)
Tournament golf is such a small portion of the game, I don't think so, but many would consider a challenge suitalbe for the best players in the game a prerequisite.
Is it realistic to separate the golf course from the golf experience? Remember, this is not art in a museum (behind a glass case), but rather the playing field for a game/sport
I think so, if you mean the periphial experience to golf. An example is Palmetto in Aiken, SC. Not presumptious, modest clubhouse, etc. Sand Hills would be a modern example of the same idea. Although the facilities are nice, your experience really starts on the first tee.