I looked up the AZ state statutes, specifically Sec. 12.4, which is the Game and Fish section. I was directed there by the AZ Hunting Regulations book that is prominent on the G&GF website. Whenever I want to search a long document like that or the statutes I just use the Search function in Google Chrome. It's the 3 horizontal dashes icon in the upper right of your screen. Just type in "muzzleloader" and it will highlight every occurence and the arrows will jump to the next occurence for you.
ARTICLE 3. TAKING AND HANDLING OF WILDLIFE
R12-4-301. Definitions
“Muzzleloading handgun” means a firearm intended to be
fired from the hand, incapable of firing fixed ammunition,
having a single barrel, and loaded through the muzzle with
black powder or synthetic black powder and a single projectile.
“Muzzleloading rifle” means a firearm intended to be fired
from the shoulder, incapable of firing fixed ammunition, having
a single barrel and single chamber, and loaded through the
muzzle with black powder or synthetic black powder and a
single projectile.
I could find no reference to any restriction on muzzleloaders. However, this is the AZ Administrative Code and it may be that there is a restriction not listed here, I don't know. I would call AZ G&F.
Here's something else I found in the administrative code that I didn't know:
A “muzzleloader” season may use one or more of the following
methods or devices if authorized under R12-4-304
as lawful for the species hunted:
a. Bows and arrows;
b. Crossbows or bows to be drawn and held with an
assisting device; and
c. Muzzleloading rifles or handguns, as defined under
R12-4-301.
I don't know when a muzzleloader season might be easier to draw than an archery season, but maybe you're an archer who wants to hunt with a smoke pole toting friend but you don't own a muzzleloader.
Or, you own a crossbow but know that you can't use one during archery season. You just apply for muzzleloading season.
Again, I would check these things out with the AZ G&F.