I have a hunting buddy who flies out to colorado every year to elk hunt with me. The upside is he saves so much time compared to the 2-day drive, the downside is meat management and transportation and ultimately $$$$.
Once he is out here, I am his transportation, so that is not a big deal. If you don't have a friend that lives there, you've gotta rent a 4wd truck/suv.
When you fly you are limited on gear. We backpack hunt, so he has his frame pack filled with all of his gear and also checks his rifle case. His carry on is filled with regular clothes to wear before/after the hunt. He is maxed out with what he can carry.
Then he shoots an elk, we bring it back to my house and butcher it ourselves in a day, straight into my deep freezer. Takes a full day to get frozen solid, then I have two spare coolers that he packs the meat into... then flying home he has to pay extra baggage fees to get it home. Fees get even higher if the coolers weigh over 50#'s each, which they often do.
Couple years ago he did not have time to butcher his elk after the hunt, and we took it to a butcher. he flew home, and I had to pick the meat up for him, box all of it up into a special foam-lined box, and next-day air the huge box out to him. With the butchering fees, special box and shipping it was darn near close to $1,000 to get the meat back to him... and impossible if I were not out here.
I have personally flown with a rifle dozens of times and never had a problem. I do not see that as any type of problem.