Free: Contests & Raffles.
Muzzy also offers the fewest GMUs, and from my experience they have been the most crowded.
Probably because it requires the least amount of effort of the 3 to do. Not that a rifle hunter don't put in their time, but generally archery and ml take a lot more practice and time to be successful with.
Archery takes more dedication, as you need to practice shooting on a regular basis. With a rifle you can never practice and still be good out to at least 200 yards. Muzzleloaders also require more dedication and more shooting time to work up an accurate load and to get sighted in properly. The biggest drawback in my mind is the open sights. Second drawback is you never know if it's actually going to fire.
At least for me, it is a totally different reason than any listed above. I used to archery hunt and was successful. My son was 7 at the time and I could not effectively hunt(hard) with a 7 year old toting along. Also, my father in law was getting up in years.I wanted my son to be able to enjoy hunting with his grandpa(rifle hunter). I believe it is important for my son to experience time with family out in the woods. When my father in law is no longer able to hunt, we will go back to archery.