This is a bit of rehash of somethng I typed out to somebody a whle ago in relation to a similar set up, the person needed things over simplifed so excuse it if its been dumbed down too much;
So think of the filter as a toilet with a septic system.
You have several ways of managing the waste but at the end of the day the goal is for it not to interfere with your life.
Filter wool, sponges and protein skimmers are mechanical filtration so they dont break the waste down they are designed to aid physically removing it.
Imagine songe placed in the first section of your filter as putting a piece of fly screen across your toilet seat. liquid waste will pass through but solid waste will be caught there. Now if you remove that fly screen every 24 hours, throw away the solids and bleach the fly screen to sanitize it, well this is a method of dealing with waste. But leave it there for weeks.... months and keep building up solid feces, you will have nasty byproducts dripping through the fly screen to the next stages but you are in a pretty bad situation.
Now think of protein skimmer as a mega industrial exhaust fan in your bathroom, nearly all liquid waste is removed straight away before it has chance to be of any issue and a fair chunk of the solid waste is as well. Its effectively doing the job of removing the waste before it causes any issues but without you having to get your hands as dirty and as regularly.
If you put the fan (skimmer) after the fly screen it will catch some of the liquid and nasty stuff that drips through but it doesn't solve the issue that you have a pile of nasty stuff causing issues.
Now whatever gets past these mechanical layers has to be dealt with by biological means, same as a septic system.
Think of this as a society. There is a delicate balance with different people performing different jobs.
The people doing the hard work at the front of the process, they are the first to pop up in any new place, reproduce the quickest and can live in vast range of conditions. On your glass, surface of rocks, on the fly screen with the feces you name it.
Then we have middle management, they take a little longer to pop up and are slightly more fussy where they live and take alot longer to reproduce.
Then you have your upper management. They take along time before they appear on the scene and focus on dealing with the high level problems, they reproduce very slowly and require very specific conditions to live in. They refuse to live in houses like sponges or amongst the front line and middle management and will only be found deep in the center of live rock, deep sand beds and marine pure blocks and so on.
So assuming you have your housing sorted out you have a pretty balanced society but there is problem of excess, so we start interfering chemically by adding vodka (carbon- nitraguard) They all reproduce a lot more.
Now if we remove the vodka really quickly everybody realizes they have 20 kids in a 2 bedroom unit and things become messy. But now we have a situation where people are breeding too quick beyond the amount of work there is. If they starve they die and create pollution so when ideally want to remove a bunch of these people so we remove (skim) them out and they take all of the waste they have built up with them. If we didn't remove (skim) them, then adding vodka (a carbon source) would only cause issues so the two need to go hand in hand.
We can also manage the problems directly with chemicals such as the phosphate pads etc in the same way a nuke does, this should be the last line of defense.