To compare cars or your own living room with a working ecosystem is rather pointless. If you should compare an working aquaria with anything - you should compare with mother earth. And she runs skimmerless

I have run a lot of nanos and aquariums without a skimmer for years. I have got some experiences with this. It works very well but one backslash with mature aquariums (a high load of corals) is that the same thing can happen as with very well planted freshwater aquariums. During night time - the consumption of oxygen can be very high leading to an oxygen defiency. It has happen to me in a very well "planted" reef of around 25 gallon. I lost a lot of fishes that night. In this case - a skimmer works as a gas exchanger and can be able to maintain an oxygen level around 80 - 90 % during night time. There is one article where someone have tested this and shown that a skimmer maintain a level of 80 % saturation of oxygen during night time. I do not remember where I read it - maybe
@Sallstrom remember the article (he is younger than me

) There is a lot of examples that show that a good skimmer can both put in and take away CO2 from the water. It is probably the same with ammonia gas (ammoniac, NH3)
IMO - the skimmer is mostly a gas exchanger equipment - as some pointed out - the nutrient export from skimmer is limited - you need to use other methods.
In my present aquaria - I use a skimmer in order to serve as a gas exchanger - I´m not collecting any skimmate - it goes back to the return chamber of my sump and up to the aquaria again.
For a prolonged period (> one year) I run the skimmer very dry - I clean the skimmer cup every 2 to 3 months. Since around 2 months ago - I run the skimmer at max (both pump and air intake) and let the skimate going back. And yes I do not do any WC. I run without WC for one year - in January I had to fix my remote DSB and did a 50 % WC. Since that - no WC again.
I would gladly run without a skimmer if I could fix the gas exchange in another way - with a trickling filter or a downstream skimmer (they are the same construction). But for now - the skimmer is my only option.
Honestly - I have a problem with PO4 and NO3 -
they are to low and I need to dose PO4 and NO3 every day. And the stocking is not ideal either - around 40 fishes - 80 gallon. + 40 hermits, + 70 snails. See my build thread in order to understand how awful this aquarium look like because the skimmate goes back and no WC.
Sincerely Lasse