I too have wondered about this. I’ve hunted cow elk only once and got very lucky, so I have no claim to expertise here, but I’ll share some thoughts.
One thing mentioned often is mental toughness and discipline, which is a general skill that applies to any challenge in life. Will you still be able to will yourself into hunting with the same focus on day 5 as in day 1? Will you be able to get up uncomfortably early, in the cold, and get to your hunting spot before sunrise, day after day? After covering many miles with no sightings, will you still step softly and keep eyes on the horizon? Will you be able to handle the loneliness, if going solo? Will you let your less enthusiastic buddies drag you down, if in a group? Will you have it in you to move on to plan D after A B and C fail, the weather gets crummy, and your bed at home is calling to you?
A lot of these challenges can be lessened by practical decisions. Take a short mid-day nap so you’re not drained every night and fail to wake up early. Eat well. Stay warm and dry. Hike light. And, of course, being physically fit means that you will be able to handle the challenges much more comfortably.
You can also practice and prepare. If you’re going to be waking up at 5 am every morning, then by god don’t let day 1 be the first time: start getting up early before the hunt starts. Hike - a lot - and in the rain and snow. Do some weekend backpacking trips to get used to the feeling of being out there for days.
Then there are the qualities specific to hunting and to elk. Did you do enough research and scouting to pick an area that is likely to hold elk? Are you good enough with your weapon to take advantage of the few opportunities you’ll get (eg short time windows, unsupported rifle positions)? Can you spot, stalk, and still hunt effectively?
To summarize, I think a successful hunter has a mix of general qualities, which tend to make you succeed at any outdoor challenge, and more hunting-specific qualities, which you mostly learn by getting out there and learning by experience. I’m not sure which overall set is more important, but if I had to guess it’s the former. The guy who has the grit to stay out and hunt with focus and determination for days on end is a lot more likely to punch his tag, even if he’s not exactly an elk genius. Let me know if I’m totally wrong.