I think the reason you don't often see the "do nothing" approach is largely a historical one. When I first started in the hobby, the recommendation was either to do nothing or to reduce nutrient levels. I had a few buddies that chose to let things play out and one tank I was called in to work on from an owner that hadn't touched it in months beyond adding top off water and feeding the fish. In all of the cases, those that did nothing often ended up losing of their corals as well as some other animals. Two of the cases were for ostreopsis, which is decidedly more toxic and at least one I scoped out as amphidinium. Anyway, I know my little anecdote is only an n=4, however from what I've seen personally as well as the reefers I've talked to who said they didn't do anything and did have amphidinium, I don't think letting the tank reach "equilibrium" has proven to be an effective stratedgy. I'd love if the Julian Sprung model of disturbance/equilibrium/homeostasis/stressor was effective for these dinos, but I haven't seen any evidence to that effect.
That being said, if you want to run the experiment, I'd love to follow how it goes
I've been on the dino train for 5+ years now, half my tanks never had issues the other half do. I was one of those who dosed bleach back in the day along with the metro when Tillward was experimenting. During these years all the threads and my personal experiences, I've never lost a coral to Amphidinium Dino's. I've lost corals to the changes / things I've added. Since this thread is for Amphidinium, we are not concerned with toxicity and the waiting game may be the solution to this strain. We always want a solution, and solutions in a bottle are becoming bigger thing as this hobby evolves, just not sure it applies in this case. I'd love to hear good news but, I'm going to take a step back and keep my corals alive while others mess with concoctions.