I don't know firsthand, but I'd bet money that the primary reason for the bucket system is historical. Or in other words, the origin likely comes from paper or early computer based inventory tracking practices.
These days, the availability is theoretically based upon the "options": flexibility is one, but so is the ongoing aggregate number of passengers. The airlines charge a "starting" cost which is supposed to fill the plane to some minimum capacity and revenue which pays back operating costs. The risk that this doesn't occur is why flexible fares are more expensive. Biz/first class usually combine more passenger space = less overall passengers = more cost per passenger, plus more service plus flexibility.
In reality, the bucket system today is more a function of system complexity - which is to the airline's advantage - but offset by the advent of OTA booking engines.
The rise of Spirit, for example, is because they game the OTA booking engines by unbundling almost everything into fees, but which makes their fares always the cheapest.
And then there's the mileage folk - who gamed the system back in significant part due to the fare buckets, although the advent of revenue based earn has largely negated that.