What if your ATS reduces nutrients too low?

You have it right, the key to getting the nutrient level you want (at least nitrate) is by tuning the settings of the scrubber in synch with the amount of feeding. I am not a proponent of "feeding the scrubber" because to me, that is something that could potentially cause more problems in the long run.

One thing to remember is that in the ocean, where there is a virtually unlimited "nutrient sink" of water, you don't typically have high levels of N and P. Not saying that's the case everywhere, but (I recall) in most areas this is the case - and corals do fine. The other difference is that while they are in nutrient-low water, there is typically also a constant food source flowing past them. These are major differences between an open (ocean) system and our closed (tank) systems.

Ideally, you want to keep the food circulating without excessively raising the nutrients. In a closed system, this can prove to be difficult. Add in that everything contains phosphate on a cellular level (in the cells - which you can't rinse away) and the food we feed is inevitably processed in some way, and that (mature) reef tanks have anaerobic bacteria that reduce nitrate, you are left with excess phosphate without that natural reduction mechanism like there is for nitrate (at least, not one that is very effective)

It's my belief that this is the reason that the "zero nitrate but readable phosphate" situation raises it's head more often than the reverse situation.

Some have resorted to adding nitrate in various forms. Feeding is one of these, but this also injects more phosphate into an already unbalanced system. The other option is to dose something with nitrate in it, like Potassium Nitrate stump remover (the powdered kind, there is one specific brand of Spectracide that I believe is the only one you want to use) or Calcium Nitrate (which is a freshwater planted tank supplement/fertilizer) and to me, these are better alternatives than "feeding the scrubber"

The other option is, of course, phosphate removal media. A combination of phos media and nitrate dosing would likely lessen the impact on the wallet overall.

Also keep in mind that phosphate stability is more critical (IMHO) than phosphate level control. While some corals don't respond well to elevated levels of phosphate, most corals don't respond well to rapidly changing phosphate levels. So the key is to take it slow, get to where you are comfortable, and try to stay there. By "rapidly changing level" I am referring to the use of "shock" methods like precipitators such as SeaKlear (Lanthanum Chloride). These will give you the quick fix but your corals will rebel (RTN, STN, etc)

Most people also forget that their corals both take up nutrients and give off waste - not in the voluminous amounts that fish do, but they still do. Display tank photocycle is therefore a part of the nutrient uptake equation - reducing your lighting will reduce your coral nutrient uptake (and growth rates, etc)

Taking all of this into account, you can see why it's difficult to come up with a boilerplate answer to just about any question, but I hope that all helps somehow!