The booking code has primarily been an inventory control mechanism. Inventory buckets are switched on and off here. The fare basis code and fare class determine additional rules associated with the fare that can also limit its availability and usage.
95% of the time, the booking class is the same as the first letter of the fare basis code. But obviously 5% of the time corporate fares are used where flexible fares can be sold but have availability limited by a lower inventory bucket.
There are other reasons and usages too. Most of which I don't know about. I will reach out to an airline person to get additional information
So I did get a response back from American who confirmed my understanding. Hope this helps
"I heard back from RM and they confirmed that at a high level, the booking class is used for inventory and the fare class (fare basis) contains the ticketing rules/restrictions.
To your point, if a class is still available, one still has to be able to meet those specific fare requirements."