I think it might be possible for WGT to regulate this - I have been carrying a sleeve of balls that were rated higher than my tier/level when I tried to enter a tournament. When I tried to tee off, I got a message that I could not play because I had equipment higher than my tier (I think it was a set of Callaways I had that were rated for Legends).
If the tournaments can be set up to recognize that, I think recognizing that a player has anything but the starter equipment in the bag should be doable.
FWIW - I tried playing Olympic with just the starter ball - boy was that a great lesson in learning the slopes on the green to use roll-up shots when I'm normally able to stop shots well on the greens...