For my tank of many fish and mostly SPS with a few LPS, my target for phosphate is 0.1-0.2 ppm and my target for Nitrate is 10-20 ppm. I only started running chaeto after regular water-changes didn't keep those values in check. I always ran a skimmer, but it didn't always take much out in the early months.
What you want to be very diligent about is not letting your phosphate (PO4) or nitrate (NO3) levels go to zero. Undesirable things happen to your tank when either of those are zero that can take months to recover. To this point, you shouldn't run chaeto if the effect of it is your phosphate or nitrate get completely removed. A young tank or a lightly-stocked tank doesn't always require every nutrient-export method to be running. If you want to run chaeto with low levels of PO4 and NO3, then just keep the chaeto small. The duration, color, and intensity of the light also affects the growth of chaeto.
Lastly, if your trace levels of Iron go to zero, then the chaeto will die. It may takes months or years (or never) but if your chaeto gets big and grows fast, then it may consume more iron than your water-changes are replacing. This happened to me and it took me 6-8 months to remove all the excess phosphate ( >1.0 ppm) from my system (it binds to your rock and sand). When my chaeto died, it turned grayish-white, thin, and limp. I didn't know at the time what that meant so I try to pass it on to others. It has never died again after I started dosing small amounts of iron, since around 1 1/2 years ago.