For me - it is not a question of removing whatever (IMO - a skimmer remove proteins, amino acids and to a very small amount small particles - mostly nothing else) - it is a question of gas exchange! Modern skimmers are the best gas exchangers per area constructed. But I can see a lot of crap build up in the collection cup says friend of order. Yes - but put a cup of protein and nutrient rich water together with maximum oxygen availability in 25 - 28 degree C for a couple of days - you will be surprised of the result. Cut the oxygen supply - observe the colour change and the smell.
IMO - the most of the craps seen in a skimmer collection cup is fabricated in the cup with help of bacteria and nutrient rich water. Skimming wet (lot of oxygen rich water coming in) - one result - skimming dry (not so much oxygen rich water coming into the skimmer cup - another look and smell of the skimmate.
Since my start as an hobby aquarist back in 2006 i have been known as the "no skimmer guy" in the Swedish reefing scene. I have run aquaria from 5 gallon to 90 gallon without a skimmer. It was a big surprise for many when I in my new build incorporated an oversized skimmer. The reason for this is that my construction is build on biological processes - and they demand oxygen. I get a little extra oxygen through using an oxidator but during nights (without so much internal oxygen production from my time reversed refugium) i can´t know if the oxygen in the aquaria will be as large as the demand from corals, bacteria and other inhabitants. I have been out for a large fish kill in a 40 gallon aquaria probably because of oxygen depletion during night - no skimmer - no fuge but total overgrown of mushroms, softies and so on. They will be net producers of oxygen during the light period but net consumer during the dark hours. With this tank - I planed a dens coral growth and rather much fishes (I have 40 + in a 80 gallon system but small ones).
There is alternatives to skimmers - fast flowing bio towers (also known as downstream skimmers - which is a variant). However these demand a height that I did not have. People with sump in the celler could test this type of gas exchangers, Basically a pipe open in both ends but containing bioballs (or similar things) Air coming in at the bottom - going out in the top (for an effective one - use a fan). Water coming in at the top - out in the bottom. The filtermaterial in the air (inside the pipe) - a fast to very fast flow creating a thin water film on the media and also polish the bacteria film at the media (hence fast flow). This construction will also create a steady flow of bacteria into the system, hence providing hungry polyps with bacteria food. This was my wish - but I could not this time construct such a system in this aquaria.
In a system like mine - there I want to keep most nutrient inside the system - recirculate them - and harvest biomass as Chaeto and corals in the end - there is a pair downsides with heavy gas exchanging 1) I will lose N as NH3 to the air. This is the reason why I directly calculated with adding N as NO3 during normal running when the whole biological concept was working. The concept include anaerobic breakdown too, hence denitrification - more losses of N
2) I will be sensitive to the carbon dioxide level in my apartment. If my grandchildren visit me - the pH of the aquaria will go down

The last one - nowadays - I´m not sure if it is a negative thing because all of my efforts to keep the pH up with other methods have result to a normal pH swing of 8.2 - 8.4 (two person and one cat). With grandchildren staying over 8.1-8.3 - hence they are helping the system getting more CO2 during photosynthesis.
Currently - I´m running an oversized skimmer - but the skimmate goes back to the return pump chamber in my sump
What´s my answer

? Basically - yes you can do it but be aware of the oxygen levels during night - especially if you have a lot of fishes and corals. The corals will help you with the oxygen during daytime but during the dark hours - you will be forced to pay back.
Sincerely Lasse