Running a business successfully in and of itself would not qualify someone to be an AD. Other than both entities wanting to be in the black - an athletic department is completely different than other companies. From the NCAA rules, to dealing with contracts, fundraising, facilities, etc, etc, etc.
I’ve never understood the rationale that some people have for putting “businesspeople” in non- business positions, and I say this as someone who’s owned a business for 20 years. Not trying to turn it political but, look no further than D. C. for a great example of someone who’s unqualified for job they were given and the negative fallout that can occur when someone’s in over their head.