I have a large tank.
I have almost 20 fish.
My skimmer pump broke about a month ago, and I have been skimmerless while I wait for a replacement. I know you are looking for a long-term answer to sustainability but after a month I can see no differences at all. I don't have any more algae buildup on the inside glass, or anything else that is out of the ordinary. I still do my routine water changes, and I have always had a fuge, but the growth on my chaeto has been the same as well. No more or less really.
My pump is expected to arrive early next week and my skimmer will be back online Monday, but I could not see any noticeable changes from running without one at least in the short term.