As
@Dkmoo answered, it depends. Really vague I know. It isn't their intent or mine to be vague but the correct answer really is "it depends".
To clarify a bit the reason why it depends is because it depends if the hobbyist designed the system to require one or not. It really is that simple. Hobbyist can design a system such that a skimmer isn't needed. It is a tool to use as is a controller, a return pump, a heater, a light, algae scrubber, and similar items. And by design I'm talking about the whole system because they all work together.
Fish load is but one question. Biological filter, corals, flow, and micro fauna are some examples that will help answer the question if a skimmer is needed. People run successful tanks without them. Some people run them every other day. Some once a week. Some daily or 24 hours. The key is the balance of nutrients both import and export. Which gets back to the design.
The hobby has come a long way from the early days with a box of water, power head, heater, air stone, and light. Set up everything with thought and a vision and a goal then the answer is yes, you don't need one because it was designed not to. And should something happen then you can always add one.
Personally speaking my first tank 20 gallons didn't have one. My second tank, 100 gallons, did. In fact I'm using that same skimmer 21 years later on my 210 gallon display. In between I've run a 40 breeder without a skimmer, 29 gallon biocubes without skimmers. And one 40 breeder with a skimmer. I think they are a valuable tool to have but at the end of the day no, they are not a requirement if the tank is setup correctly.
Just my opinion.