It's not exactly in the golf rules but in special rules for special tournaments.
From Joe Sixpackgolfer to the average amateur tournament player, we may use any combo of balls!
In WGTland, it's rather stemming from the fact that the bag is closed during play, with only one slot for balls. For the longest time, we've been allowed to "refill" through the round.
One of my pet peeves with this game is when I take my last shot on a ball, and because I don't have anymore of those exact balls, I'm stuck playing with the standard ball for the rest of the game.
Your pet peeve should be your preparation for the game.
Either you play a serious round (e.g. single play tourney) and prepare for balls lost or "worn out", or it's casual = doesn't matter too much to you, which is perfectly o.k.. In the latter case, you may quit, load a new type of balls and return to tee 1 of the course in a split second.