Don't things need to eat something before they can produce waste?
i am not. the amount of waste produced is very close to the amount of material brought in. that is the point i am trying to make. very little of the material an organism takes in is retained in its mass.
BTW, take a closer look at your simplified graphic of choice. Much of the P cycle is very much recycled, as opposed to simply being sunk into the sediment. It even shows exchange with P going from the sediment back into the water column

Storms (aquarist in our tanks) kick up sediment and organics, and of course a huge host of sediment dwelling critters (both in the ocean and our tanks) do something called bioturbation. All of which contributes to recycling a goodly portion of the P in that P cycle.
that graph was only for the P cycle in the marine environment. here is a graphic showing the entire P cycle. note the amount of arrows going into the substrate, and the number of arrows leaving the substrate.
if we look at the entire P cycle we see that P is locked in marine sediments.
i am all about stirring up the substrate in an aquarium on a regular basis, but that is not what we have been told. we are also told to setup our systems in a way that inhibits our ability to stir up the entire substrate to release the trapped organic material. we put to much LR in the system creating unreachable areas.
It's also a pretty safe bet that Randy isn't ignoring organic vs. inorganic P, and I know I'm not. Though I will admit many likely don't think of it, since organic P isn't readily tested for.
you can not test for organic P. it is impossible, but we can at least use our eyes. the more biomass and the more waste organic material, the higher the organic P in the system. what i think is missed is the main source of inorganic P, the decomposition of solid organic waste.
That graphic ignores that in a reef tank, the huge input is food falling from the sky.
what from of P is falling from the sky? or do you mean plankton?
it is not the inorganic P that needs to be worried about and it seems the hobby industry is fixated on. it is the organic P that we need to be paying more attention to
Why do you think that?
In other words, what about it worries you more than it worries you about inorganic P?
How do you decide what forms of organic P are worth worrying about, and which are not?
by looking at what is the primary source of the problem. the biggest producer of inorganic P is the decomposition of waste organic P. the dissolved inorganic P is not a big concern, if the levels are low enough, then the bacteria and micro algae will take care of that and can be easily removed by skimming.
" phosphate sorbed on clays" per the chart you selected would be species of inorganic phospahte "sorbed" at the surface perhaps some orgnic phosaphte too, ;not the phosphate that is incorporated into calcium carbonate crystal matrix .The later reduces biological availability per the paper you cited as it would obviously require dissolution and not just desorbtion via biological activity or equilibration with i phosphate levels in the water. Further it is noted that as the level of phosphate incorporated into the calcium carbonate crystal matrix increases the adsorbtion rates at the surface decrease.
So, it seems to me if the paper is correct and I'm reading it correctly that calcium carbonate could lose it's ability to adsorb biologically available inorganic or even organic phosphate on it's surface overtime but that does not mean that it releases what has been incorporated in the crystal matrix since that would require the aragonite mass to dissolve. It is sunk/sequesterd.
A likely outcome is that the sand may loose much of it's ability to adsorb phosphate on it's surface overtime but won't give much back that has already been sunk in the crystal matrix at typical reef tank pH levels IMO.
looking at the chart again. note 4 is what Randy is talking about with dissolution, and i think this is what you are talking about. no argument here. what i am talking about is the role phosphate solubilizing bacteria play in all of this. they can pull P from the matrix. this is not a purely chemical reaction.
That graphic ignores that in a reef tank, the huge input is food falling from the sky. 
It also ignores export via harvesting and skimming among other things.
no it doesn't ignore it because it is not removed in the marine environment. it gets sunk in the substrate. if you want to remove it, then here is a modified version of the same chart showing which types of P are removed using various P removal methods.
It also notes dissolution and precipitation ; the former should be minimal at aquarium pH levels for most precipitated phosphate.
confused. this graph is of the marine environment, how is that not what happens in our systems? do our systems not behave like nature? if not, then why are we trying to emulate it? which is it?

the former is done by bacterial activity. the same activity that allows "cooking" of LR. the phosphate solubilizing bacteria are doing this.
You say:
it is the organic P that we need to be paying more attention to
Not all of that is biologically availabe. How would you pay attention to it? I have no idea what % is. All of the inorganic phosphate is reactive.
all of that biomass is organic P that is available. P is in constant motion. all of the solid waste organic material in the substrate is potentially available. it just takes a little bit of stirring. this can all be converted to inorganic P. any waste organic P is enroute to being available inorganic P. it is decomposing.
you also say:
it's the mineralized phosphate that's the problem.
They are not the same thing. The mineralized phosphate is not reactive unless the mineral is dissolved which is not likely at a significant level in a reef tank,IMO
phosphate solubilizing bacteria are able utilizing the mineralized P. it is this give and take between the calcium carbonate matrix and the bacteria that keep P in flux and allows the calcium carbonate to function as a phosphate binder. P moves slowly downward through the substrate. free sites on the Calcium carbonate matrix bind P, the bacteria remove P, the bacteria die, or get consumed. more P binds to the matrix. the bacteria biomass falls deeper in the substrate through the actions of other bacteria and benthic organisms until resources become limited. usually C in the deeper reaches of the substrate when the available space between the grains is full of detritus. solid organic waste. whether it is bacterial milm or solid waste from organisms.
Phosphorus liberation by aquatic microorganisms.
Dynamics and Diversity of Phosphate Mineralizing Bacteria in the Coral Reefs of Gulf of Mannar.
these upwellings are from the disruption of deeper marine sediments. stir the substrate on occasion for a good nutrient upwelling in the system.
Not exactly, up wellings occur on reefs from a drop in water pressure under the footprint of the obstruction( the reef ) relative to the water crashing into it.As a result the water under it moves up and the void is filled with new water at the bottom passing through the substrate under the reef.This is known as advection . It' an engineering issue in bridge construction and the reason sand seems to collapse under your feet when you stand in waves. Just stirring up substrate won't cause upwelling.
it is a disruption that is releasing the trapped organic material. something that should be done more often in our systems.
G~