You are right and wrong. N and P are not nutrients... they are building blocks. True nutrients mostly come from sugars (carbon) - the corals only get these from the
zoox and if they can catch some usable food high in carbon (rare in our tanks for some corals like acropora, but very common for NPS or LPS corals) - light feeds the
zoox, but they need building blocks to reproduce too. You do not need a ton of building blocks, but you do need some - too many of either can inhibit calcification and stop photosynthesis if they get high enough.
Once all of this is understood, then you have to understand what happens when building blocks are low and true nutrient levels and elements (carbonate, calcium, strontium, mag, etc.) are high. Low building block levels increase calcification if carbonate and calcium is in good supply. Carbonate in the ocean is low and almost a limiting factor for calcifying too fast. If you really lower the building blocks too far in an aquarium, then the skeleton will grow faster than the tissue can grow and then you get burnt tips. However, even if you have a lot of N and P, you still need real energy from the sugars in the
zoox to make new tissue... so light matters too. This is only really common in cases where people are using GFO, Organic Carbon, etc. since most natural methods will take the building blocks low, but not too low. Burnt tips is not as common as it was with fewer people carbon dosing than they were five years ago. Brunt tips was not common at all before the introduction of GFO and widespread use of carbon dosing... and people kept their carbonate at 10-12 dKh all the time.
Think of it this way... you need building blocks to grow, but not to keep what you have (sustained living)... if limited with N and P, then growth slows and colors fade with decreased
zoox, but no death. If limited by true nutrient (sugars from the
zoox), then stuff can die. People blame building blocks for a lot of things because they think of them as providing everyday energy and they do not.
Also keep in mind that a lot of organisms can get nitrogen from trace levels of ammonia.
IMO, N and P play a role, in a "enough, but not too much" kind of way, but not nearly as much as true nutrients from the sugars from the
zoox. I find it amazing that people fret and fuss all the time about N and P while not focusing enough on light.
...so if a coral is starved for true nutrients and also building blocks, then it can suffer. Having too high of alk for thriving corals can be bad since they can literally outgrow their body. ...so it all kinda is connected... my apologies if this is too far of a semi-tangent on alk.