The skimmer does not pull out nutrients. Nutrients are inorganic salts, such as NO<sub>3</sub> and PO<sub>4</sub>, anions of nitric acid and phosphoric acid respectively, better known as nitrate and phosphate. They do not contain Carbon. They are ions, and do not have the molecular properties (hydrophillic, hydrophobic "poles") by which the skimmer works.
The skimmer pulls out some Dissolved Organic Compounds such as proteins, amino acids, vitamins, etc., having the molecular properties needed for the skimmer to remove them. These all contain Carbon, as well as many contain Nitrogen, and various other elements/compounds, Granulated Activated Carbon also removes some dissolved organic compounds by absorption.
Algae, both unicellular (Chlorella, and diatoms; examples) and multicellular (GHA, and chaetomorpha; examples) are primary producers. In other words, they use inorganic sources with which to build organic compounds for growth.
These primary producers use light, water, CO<sub>2</sub>, Nitrate, Phosphate, Iron, Copper, (and other trace elements) in the presence of light (energy source) to grow. They are all inorganic.
The source of these inorganic compounds is the decomposition (heterotrophic bacteria) of Dissolved organics, and secondary metabolites, (assuming you don't leave dead organic material in the system; the results of competitive chemical warfare between different species are secondary metabolites, for example.) excreted directly into the water by the critters themselves. (Unlike fresh water where ammonia NH<sub>4</sub> is excreted directly by the critters.) The result being Inorganic Compounds, namely ammonia, keeping it simpler.
Autotrophic bacteria, take the inorganic ammonia, and do their job: ammonia > nitrite > nitrate. To do a more complete explanation there are both ionized ammonia, NH<sub>4</sub> (ammonium nitrate for example) and unionized ammonia (NH<sub>3</sub>.) It is the unionized ammonia that is toxic.
Primary producers take up the Nitrate, and the "cycle" starts all over, though it never ends. Thus making the comment "my tank is cycled" one of the biggest myths in the hobby. The other big myth is "my parameters are fine."
In order to make heads or tails out of the methods, and processes, there needs to be a basic understanding of the difference between Dissolved Organic Compounds, and Inorganic Nutrients; they are dealt with in different ways, and many methods are mutually exclusive, and/or detrimental to the system, as in the case of Vodka dosing, or heavy reliance on GFO or phosban. Vodka dosing takes out the bottom end by encouraging heterotrophs to out-compete the autotrophs, making the system dependent on the organic carbon source, and if curtailed could cause the tank to crash. GFO/phosban remove phosphorus from the system, while adding iron. Phosphorus being an essential for life element.
To revisit a bit: Skimmers do not remove nutrients, they remove some of the sources (dissolved organics) of the nutrients. This reduces the burden on the rest of the system, and also reduces the biological oxygen demand. Primary producers remove nutrients via the process called Photosynthesis, releasing oxygen into the water, increasing the dissolved oxygen concentrations.
Because production of dissolved organics is way higher, and more diverse than the skimmer/carbon can handle, (the only methods of direct removal) there will never be a shortage of raw materials. Dissolved organics build up and are the cause of long term system decline. Nitrates are the result of a natural process, essential for the survival of our systems. They can be easily dealt with by a natural process. Phosphates are as well, however excessive phosphates are a husbandry issue, and are the direct fault of the hobbyist, (salt mix, feeding practices, sticking bare hands in the water, etc.) They need to be dealt with by an unnatural process.
At the hobbyist level, all of this is about controlling nuisance algae. (predominantly.) There are several things that algae require. To control the algae, you only need limit one of them. (iron and copper/trace elements aside.) You cannot limit light, water, and CO<sub2>, which leaves nitrates and phosphates. Since phosphates can be controlled by good husbandry, that leaves the area to concentrate on: nitrates.
So what do you really want (need) in the sump? I can tell you this much, you don't need all the junk you added to your sump design, stepping it back 20 years to the 1990s, and the technology craze. You don't need any of it at all, for a new start up, in the first place. How to start up a system is a seperate topic, and far too many have that wrong too.
The answer to "what do you really need in the sump" is more biology, and less technology, using methods to do not produce nitrates, (bio-balls, rock, mechanical filtration,) rather export them. Also you don't need methods that are borderline useless: UV sterilizer. Skimmer/carbon is a necessary "evil" at the current time. All the anecdote there is cannot touch that basic premise.
