Algal scrubbers, refugia, etc. are fine and excellent at exporting nitrogen
and inorganic phosphate if they are well manged . I use them. They do not , however, remove harmful organics(dissolved or undissolved); they actually produce them.
Organics are molecules which contain H(hydrogen) and C(carbon) along with a myriad of other things.
GAC (granulated activated carbon ) and resins such as purigen do remove organics as do skimmers but only those organic chains with an affinity for the resin, gac and/or air water interface of the skimmer. Managing total organic carbon(TOC) beyond just water clarity is a challenging rather new task in the hobby.
Algae uses inorganic carbon ( CO2) and creates the organic sugars it needs. Algae does incorporate inorganic nitrogen and inorganic phosphate along with the organic carbon it produces via photosynthesis in its tissue mass as it grows. Most living things in marine environs have a ratio of (C)carbon

N)nitrogen

P) phosphorous in their tissue approximating 116 C: 16N:1P(see Redfeild ratio). Algae puts out exudate which contains nitrogen,phosphorous and organic carbon and also puts out spores. It will also dump back C N and P if it decays in the tank or sump/refugium.
The uptake of nitrate(NO3) and phosphate(PO4) by the growing algae should more than offset the N and P in the algal exudate in a well harvested and and/or siphoned algal scrubber or macro algae refugium.
However,since the algae does not take up any organic carbon but converts inorganic carbon (CO2) via photosynthesis that which it exudes adds to the total organic carbon(TOC) of the tank. So absent export strategies( gac, skimming, ozone, etc) unless a massive system with large water changes is in play, TOC can build up from food, coral slime and the waste products of other photosynthetic organisms including algae and do harm.
Studies over the past couple of years have linked high TOC to coral mortality. It is thought that the excess organic carbon may skew bacteria balances toward pathogenic to the detriment of the coral's symbiotic relationship with certain bacteria.
Skimmers remove organics that have both hydrophyllic(drawn to water) and hydrophobic(repelled by water) molecues since these types of molecular chains are attracted to the air water interface. Skimming also affords enhanced gas exchange and pushes out some particulate organic material and some precipitants.
GAC it seems is even more effective than skimming at removing organics particularly when combined with ozone which breaks up organic chains perhaps increasing their affinity to GAC absorbtion. Skimming also offers enhanced gas exchange and pushes out some particulate organic and precipitant matter.
Managing nutrients in a reef tank is not just about managing nitrogen ( NH3/4, NO2,NO3,etc ) and inorganic phosphate(PO4 species) although keeping low levels is important and readily measurable. TOC must be limited as well even though measurement is not available in the hobby as it requires some rather sophisticated scientific equipment. Even though it can't be measured in your tank organic carbon is there even when the water isn't yellow and export strategies ( skimmers, GAC, puigen, ozone..)are necessary ,in my opinion, particularly if you want to keep high reef animals like sps and most lps.
FWIW, do keep one tank skimmerless( well it might as well be so since I only use a Red Sea hang on which does very little l). It's a 65 gallon which houses some non reef safe fishes that I had to have and a bunch of leather corals , discoma , rhodactis,xenia and other things that generally come from relatively high nutrient turbid waters. I do. however ,use purigen, and gac via canister filter on this tank. After about 2 years all the critters are flourishing.