It's more than algae just being a nutrient sink. It varies significantly by species but algae is dumping hydrophilic and hydrophobic DOC into the water that promotes pathogenic shifts in coral holobionts/microbiomes. Skimmers and GAC won't remove the hydrophilic DOC (specifically the Dissolved Combined Neutral Sugars, DSCN). Sponges will process DOC (and the hydrophobic as well, 1000X faster than the bacterioplankton in ht ewater) but they process DOC from algae differently than from corals and with too much nuisance algae a negative feedback loop helps the algae but hurts the coral. Stripping the nutrients out of the water also makes it harder for corals to compete against the algae so corals are getting a hit on two fronts.
DOn't feel like you need to pull out all the rock. I'd actually try to disturb the system as little as possible. Remeber the sponges are helpful and the rock that doesn't have a lot of algae might only need a little brishing. If a rock sin't integral to the aquascaping and doesn't have any sponges on the back side and no corals of value on the lighted side and lots of hair algae I may just set it outside and let it dry out. In the first thread roughly a third of the rock was removed fromn the tank and scrubbed off in aquarium water and only a couple of the worst pieces were removed a 2nd and third time to be scrubbed in aquarium water. In the 2nd thread since it was so tall and seriously needed rescaping (the previous maintenence company just pilled the rock in) over half was removed and maybe about a fifth wasn't put back in.
To help understand the roles of corals and algae and microbial processes in reef systems I'd encourage you get the book and watch the accompanying video "Coral Reefs in the Microbial Seas" (Paper back is ~$20, Kindle is ~$10) Both deal with the conflicting roles of the different types of DOC in reef ecosystems. While there is overlap bewteen his book and the video both have information not covered by the other and together give a broader view of the complex relationships found in reef ecosystems
Here's some other videos you may find informative:
Changing Seas - Mysterious Microbes
Nitrogen cycling in hte coral holobiont
BActeria and Sponges
Maintenance of Coral Reef Health (refferences at the end)
Optical Feedback Loop in Colorful Coral Bleaching
Richard Ross What's up with phosphate"
And here's some additional links:
Phosphate Deficiency:
Nutrient enrichment can increase the susceptibility of reef corals to bleaching:
https://www.nature.com/articles/nclimate1661
Ultrastructural Biomarkers in Symbiotic Algae Reflect the Availability of Dissolved Inorganic Nutrients and Particulate Food to the Reef Coral Holobiont:
https://www.frontiersin.org/articles/10.3389/fmars.2015.00103/full
Phosphate deficiency promotes coral bleaching and is reflected by the ultrastructure of symbiotic dinoflagellates
https://www.sciencedirect.com/science/article/pii/S0025326X17301601?via=ihub
Effects of phosphate on growth and skeletal density in the scleractinian coral Acropora muricata: A controlled experimental approach
https://www.sciencedirect.com/science/article/pii/S0022098111004588
High phosphate uptake requirements of the scleractinian coral Stylophora pistillata
http://jeb.biologists.org/content/214/16/2749.full
Phosphorus metabolism of reef organisms with algal symbionts
https://esajournals.onlinelibrary.w...98e60zfBEvx5IcIVGhmlpUYmzIJuqUNVm0sG8_0vth6lq
https://therichross.com/skeptical-reefkeeping-ix-test-kits-chasing-numbers-and-phosphate/
Sponge symbionts and the marine P cycle
https://www.pnas.org/content/112/14/4191
Phosphorus sequestration in the form of polyphosphate by microbial symbionts in marine sponges
https://www.pnas.org/content/112/14/4381
Indirect effects of algae on coral: algae‐mediated, microbe‐induced coral mortality
https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1461-0248.2006.00937.x
Influence of coral and algal exudates on microbially mediated reef metabolism.
Coral DOC improves oxygen (autotrophy), algae DOC reduces oxygen (heterotrophy).
https://peerj.com/articles/108/?utm_source=TrendMD&utm_campaign=PeerJ_TrendMD_0&utm_medium=TrendMD
Role of elevated organic carbon levels and microbial activity in coral mortality
http://www.int-res.com/articles/meps2006/314/m314p119.pdf
Effects of Coral Reef Benthic Primary Producers on Dissolved Organic Carbon and Microbial Activity
Algae releases significantly more DOC into the water than coral.
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0027973
Pathologies and mortality rates caused by organic carbon and nutrient stressors in three Caribbean coral species.
Starch and sugars (doc) caused coral death but not high nitrates, phosphates or ammonium.
http://www.int-res.com/articles/meps2005/294/m294p173.pdf
Visualization of oxygen distribution patterns caused by coral and algae
https://peerj.com/articles/106/
Biological oxygen demand optode analysis of coral reef-associated microbial communities exposed to algal exudates
Exposure to exudates derived from turf algae stimulated higher oxygen drawdown by the coral-associated bacteria.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3719127/
Microbial ecology: Algae feed a shift on coral reefs
https://www.nature.com/articles/nmicrobiol201661
Coral and macroalgal exudates vary in neutral sugar composition and differentially enrich reef bacterioplankton lineages.
https://www.ncbi.nlm.nih.gov/pubmed/23303369
Sugar enrichment provides evidence for a role of nitrogen fixation in coral bleaching
https://onlinelibrary.wiley.com/doi/full/10.1111/gcb.13695
Excess labile carbon promotes the expression of virulence factors in coral reef bacterioplankton
https://www.nature.com/articles/ismej2017142
Unseen players shape benthic competition on coral reefs.
https://www.ncbi.nlm.nih.gov/pubmed/22944243
Macroalgae decrease growth and alter microbial community structure of the reef-building coral, Porites astreoides.
https://www.ncbi.nlm.nih.gov/pubmed/22957055
Macroalgal extracts induce bacterial assemblage shifts and sublethal tissue stress in Caribbean corals.
https://www.ncbi.nlm.nih.gov/pubmed/23028648
Biophysical and physiological processes causing oxygen loss from coral reefs.
https://elifesciences.org/articles/49114.pdf
Global microbialization of coral reefs
https://www.nature.com/articles/nmicrobiol201642
Ecosystem Microbiology of Coral Reefs: Linking Genomic, Metabolomic, and Biogeochemical Dynamics from Animal Symbioses to Reefscape Processes
https://msystems.asm.org/content/msys/3/2/e00162-17.full.pdf
Differential recycling of coral and algal dissolved organic matter via the sponge loop.
Sponges treat DOC from algae differently than DOC from corals
https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/1365-2435.12758