Under the USGA and R&A there is no rule that says that you have to play the same brand of ball if one needs to be replaced during general play, but you have to play the same ball until there is a condition which prevents it such as: OB, Lost, or damaged ball.
The concept of a "one ball rule" or "one ball condition" is a special rule generally invoked during high level professional or amateur tournaments that requires ball replacement to be the same brand and type as the original. It appears that WGT believes every round played is subject to the one ball condition.
I find this troubling since replacing a lost ball with a "starter" would violate the so called one ball condition, but it is better than DQ'd or stroke penalties.
The OP is making a comment that most of us have had - which is why do we get stuck with a starter ball when we need to replace a ball particularly when we have a better ball in our bags.
Some players say it is your own fault for not minding your caddie when he/she warned you to buy additional balls, which is really silly. There are a number of reasons why one would choose not to purchase additional balls at that time - like say, a player has 100 other balls in his/her bag from which to choose?
Again, in general play there is no rule that says you can't use a different brand ball if you need to replace your original.
So it would be nice to use other balls before being forced to use a starter.