Not talking about nitrifying bacteria necessarily. That's a given.
Bacterial growth in general. Requires Nitrate, phosphate and carbon. When any of them are a limiting factor bacterial growth (think tissue mass, not nitrifying capacity) slows and the uptake of all those nutrients slows or stops. *again, I'm not at all talking about nitrifying bacteria's capacity to nitrify. This is about all sorts of bacteria growing and taking nutrients up into that bacterial biomass, not that bacteria consuming / converting ammonia to nitrite to nitrate*
When all are present and available, misc bacterial growth takes up nitrate and phosphate into bacterial biomass, which then can be skimmed out AND consumed as food. Ie, both managing waste and providing food for corals and inverts.
A very common scenario when organic carbon dosing (which is more effective at reducing nitrate than phosphate) is that nitrate gets low or "bottoms out" but phosphate doesn't. Nitrate has become the limiting factor (no longer Carbon as the limiting factor), and then any nitrate that is produced is quickly taken up and the levels stay at a testable zero. (nitrate and phosphate both being taken up into bacterial biomass, but that process stops when the nitrate becomes limited again, but the phosphate is already abundant so it keeps accumulating). Hence the common issue of needing GFO or Lanthum C to manage Phosphate while nitrate hovers near or at zero.
Simple anecdotal observation - My system is generally running phosphate around .1, and nitrate at zero on the tests. If I dose sodium nitrate and wait a bit, I see detectable nitrate right away, and in a week or so my phosphate testing shows a clear drop, and the nitrate I just boosted also drops. If I don't add the nitrate, my phosphate stays quite steady. Perhaps just confirmation bias, but this is consistent with and predicted by the thinking above, and with talk in other venues of "bacterial driven systems" or whatever one might choose to call this.
