I see another, more mundane reason behind it.
The "bag" has only room for one type of balls. WGT wants to follow the Rules of Golf which state that no club may be exchanged during a round (except for reasons that don't apply here). Therefore, the bag is locked during games by some software code - no access to the inventory. The ball "pocket" is one collateral damage here, as access is locked with the clubs.
In addition, I consider the inventory to be "in my garage" - out of reach.
Some have voted for a beer cart with a beer cart girl to patrol the courses - she might have other balls with her, at exorbitant prices!
Alas, no beer cart girl... :-(