It may be better stated as to what should the BCA do?
IMHO, I believe the organization that is currently called the BCA in Colorado, should change their name. Because they represent the manufacturers, and other industry members, it is in their best interest to create a better identity for their purpose. It is always confusing for people to use BCA and BCAPL and not be able to distinguish the difference between the two.
To the integral question of exactly who is the governing body of pool in the United States, there isn't one.
There isn't really a need for one right now.
It would be like the other proclaimed governing bodies of the past 20 years, existing for organizations to collect sanctioning fees for pro tournaments, without really doing anything for the money. Presenting the next get rich quick scheme for pro players who can't see the ponzi schemes for what they are. Establishing rules for events, and then altering the rules to suit one person or the next. Or the worst reason of them all, Olympic Recognition!
Unfortunately, pool is a very territorial entity. Each organization covets their hard earned membership and isn't sympathetic to an outside entity wanting to "govern" them. In order to establish a distinct ruling body, every organization would have to voluntarily agree to allow this, and be willing to support it financially. The question will be,"What do I get for my money?"
As it always has been.