We can only equip our bag with 1 make/model of ball before we start a game. Once the game has started we have no way to 'equip' our bag with a different make/model of ball.
I do not know what WGT would have to do to their game program to allow doing what you propose, but I suspect having the code in the game for every ball make/model WGT provides would bloat the program considerably.
WGT provides a pop up notice when we start using the last ball of the make/model we have our bag equipped with.
And.
WGT gives us a chance to buy another sleeve of that make/model of ball right then and there.
So be it if you choose to not take advantage of that opportunity.
Most WGT games are designed/conducted like tournament golf. Many non-PGA tournaments choose to invoke the One Ball Condition.
Also note that many of the courses we play are US Open venues and the USGA conducts many amateur tournaments where the USGA invokes the One Ball Condition. In the past I have played in local, state and regional tournaments conducted by other tournament committees that chose to invoke the One Ball Condition.
The One Ball Condition states the same brand and model of ball must be used:
(i) “One Ball” Condition
During a stipulated round, the balls a player plays must be of the same brand and model as detailed by a single entry on the current List of Conforming Golf Balls.