Even without a duplicitous P1, adding players after P1 plunges would give a favorable bias to P1. Suppose players could be added if the mistake is noticed anytime before P1 loses B1, otherwise a new game is started. If P1 is having a long ball time (good ball), it’s more likely a bystander notices the mistake and more players are added and the game continues. If P1 drains quickly before anyone notices the mistake, then a new game is started once it’s realized. The effect is P1 is more likely to keep a good B1 and discard a bad B1.
Therefore, once it’s decided that P1 playing out a single player game is not an acceptable rule, then it follows that players cannot be added after P1 plunges B1 should be the rule if fairness is to be maintained.
Another aspect to this is that P1 could duplicitously start a single player game and use B1 as practice without penalty. The opponents can counteract this action by ensuring that the correct number of players are added before P1 plunges, and in fact it’s their responsibility to do so, as stated in the rule. If the opponents do not ensure the correct number of players are added, then P1 gets free practice and the opponents cannot complain.