Why do you think NO3/PO4 are more important? More curious because it used to be everyone wanted 0 and now we are starting to see just the opposite with awesome or thriving tanks with numbers on the positive side all over the map.
I think Alk/Cal/Mag are seen as more critical due to the fact they are required for a healthy reef over time as the tank matures. New tank they may not be as important so NO3 and PO4 take priority but over the year as aquarium, rocks, and coral mature and grow they lessen and ALk/Cal/Mag take over.
Just the way I see it anyway.
Perhaps I will try to answer this with my 'novice' understanding and let the experts who have commented elsewhere on this thread correct any (likely) misunderstandings. I realize that there is a massive amount I don't understand here. Moreover, I know a lot of what I am saying is a (potentially dangerous) oversimplification. Criticism would be greatly appreciated to further my understanding.
My understanding is that there are two primary 'loops' or processes that must be managed to maintain reef aquaria: the encrusting process (KH/Ca/Mg) and the photosynthesis/nutrient process (Carbon,Nitrate, and Phosphate).
Encrusting process (KH/Ca/Mg)
I dose a 'balanced' 3-part Balling KH/Ca/Mg solution. My chemistry knowledge is somewhat weak, but my understanding is that these three parts (each consisting of one or a variety of salts) get consumed during the encrusting process at the same rate. As such, the best practice is to dose all three parts in equal proportion, to a target alkalinity.
As such, alkalinity is critically important to measure, while Ca and Mg need only be measured occasionally to ensure levels aren't getting off-balance- and in my (6 month, admittedly) experience, that has been the case. My Ca levels are ideal, and my Mg levels are slightly high but reasonable, despite little testing and no active management of either.
In sum, this process can be managed quite well by just measuring alkalinity, with monthly (or longer) checks of calcium and magnesium.
Photosynthesis Nutrient Process (Carbon,Nitrate, and Phosphate)
All photosynthetic life requires consumes C(in varying chemical compounds), NO3, and PO4. Moreover, may life forms seem to do so in a specific ratio, or range of ratios. One example is phytoplankton, which consumes those chemicals in a ratio known as the 'Redfield Ratio'. Various life forms consume those chemicals in different ratios.
The primary way these nutrients are introduced into the aquarium is via feeding, after digestion and processing through multiple processes and means.
Having plentiful amounts of all three nutrients is rare in an aquarium, as various life forms quickly multiply (bloom) to consume them, assuming conditions (light, toxins, etc) are otherwise favorable. Instead, most aquariums are 'limited' in the available amounts of one, two, or all of these nutrients, which are replenished through feedings.
Life forms that require C : N : P ratios with the least reliance on the 'limited' nutrient seem to thrive. Dinoflagellates seem to thrive in N and P limited systems. (Hair) algaes seem to thrive in C limited systems (where N and P are plentiful). This latter phenomenon is why carbon dosing is so commonplace.
This is where my knowledge, and perhaps the collective knowledge of hobbyists, seems to get fuzzy. But what we do know is that keeping low-but-measurable levels of N and P seems to be correlated with success. High N and P levels are indicative of a carbon limitation, and leave the system susceptible to excessive algae growth. Zero N and P levels leave the system susceptible to dinoflagellates, and negative impacts to corals due to nutrient limitation. While there are examples of successful aquariums that fall outside of these guidelines, they nonetheless are a good target for most aquarists.
The challenge is that unlike the encrusting process, the inputs to the system (feeding) can't be closely controlled, nor can the outputs (photosynthetic growth). Inconsistent feeding or changes a systems' fauna (such as chaeto accumulation or nuisance algae) can throw these levels into a range where many aquarists have noted negative side effects. It seems necessary to constantly monitor these parameters and make necessary adjustments to nutrient imports (feeding levels, and dosing if need be)) and exports (chaeto amount, skimmer operation) on a regular basis.
Conclusion
The above is why it seems that alkalinity (for monitoring the encrusting process), and NO3/PO4 (for monitoring the photosynthesis process) seem to be the 'big three' to me that need monitoring on a regular basis.
Criticism appreciated!