Water changes are the only way to get rid of the hydrophilic DOC that isn't removed by skimmers and GAC. Additionally, since corals and algae are promoting different types of microbial processes in the water through different forms of DOC they are releasing by redusing all the types of microbes in the water water changes allow have the potential of assisting corals in maintaing the microbial processes beneficial to them.
Here's links to some of the science:
Maintenance of Coral Reef Health (refferences at the end)
Aura-biomes are present in the water layer above coral reef benthic macro-organisms
https://www.ncbi.nlm.nih.gov/pubmed/28828261
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
Elevated ammonium delays the impairment of the coral-dinoflagellate symbiosis during labile carbon pollution
(here's an argument for maintaining heavy fish loads if you're carbon dosing)
https://www.sciencedirect.com/science/article/pii/S0166445X19307192
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
Allelochemicals Produced by Brown Macroalgae of the Lobophora Genus Are Active against Coral Larvae and Associated Bacteria, Supporting Pathogenic Shifts to Vibrio Dominance.
https://www.ncbi.nlm.nih.gov/pubmed/27795310
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
DDAM Proven
https://www.nature.com/articles/nmicrobiol201642
Coral Reef Microorganisms in a Changing Climate, Fig 3
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7096749/figure/fig3/
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