What do you think "outcompete" means in the context of evolutionary biology? Something is going to set up shop in your mouth; it's just too attractive an environment to be left fallow. Whatever that ends up being without intervention has by definition outcompeted all the other contenders. So if the good bacteria don't persist, then by definition they have not "outcompeted" the competition.
Guess the main point is the environment itself changes depending on what you do and what you eat. So you need to constantly resupply the initial good bacteria for them to keep holding on
Is there any reason you can't just propogate and cultivate them in a seperate breeding receptacle for an unlimited supply like people do with SCOBY or whatever for making sourdough and kombucha?