chaeto not growing....

correct.

skimmers don't skim out nitrates by themselves, they skim out nutrients that are bonded to something. According to Dr. Ken S. Feldman, all we are skimming with our foam fractionators may just be diatoms (see this article: Feature Article: Elemental Analysis of Skimmate: What Does a Protein Skimmer Actually Remove from Aquarium Water? | Advanced Aquarist's Online Magazine). It could be that your filter sock is trapping the same diatoms, so it just becomes another method of removal. Even if Dr. Feldman's presumptions are incorrect, the skimmer is still removing the nutrients that are bound TO something like detritus, bacteria, etc.

If you remove the sock filter that is trapping detritus and diatoms, then sure some of that will get stuck in the cheato ball. As it decays, the cheato will very likely use up those nutrients, and you will have cheato instead of detritus and diatoms. But, if you are removing the detritus and diatoms from some other means, then the cheato is only going to use the nutrients that are available in the water.

I never reached 0 nitrates when I ran just cheato, so I don't know if it is the most effective means of nutrient export. I use a skimmer, filter pads, cheato and solid carbon dosing to achieve 0 nitrates... Also, the amount of cheato you have may be so small that it is not able to keep up with the amount of nitrates your tank is producing.

It took my cheato a while before it took off, so I would suggest being patient, let the cheato grow out a bit and try the suggestions above, more flow and more light... because other than nitrates and phosphates, that is ALL that is required for it to grow.

Also, you may want to try running the light 24/7, as that is what I do with my fuge, and I get great growth now.

 

I use a couple 23w cfl lights natural light (6700 I think) and if I had some powerheads blowing it around I'm sure it would do even better.