A filter can serve several purposes that tank maintenance can't.
First of all there is mechanical filtration. Mechanical filtration will remove the particulates you have floating in the water. This can be food, fish feces or the detritus you stirring up while vacuuming the gravel. It can also remove some of the proteins that cause film on the surface of your water.
Next is the biological filtration the filter provides. It provides a stable home for your good bacteria to colonize. Without this, anytime you vacuumed the tank and disturbed the substrate you may be removing and killing off the bacteria you need to keep the water quality stable.
Third there is chemical filtration. Chemical filtration can remove odors, ammonia and other potentially toxic gases and elements from your water.
Finally there is the aeration aspect. Water moving through the filter is being oxygenated as it flows through it. The outflow into the tank also improves the water's oxygen uptake. Its disruption of the surface tension can also keep any protein waste from coating the surface of the water.
I'll have to disagree with many of your points:
1.) Mechanical filtration isn't totally necessary in a tank at all. Most salt water tanks
forgo mechanical filtration because trapping a lot of organic particles in one spot makes a nitrate factory. Additionally, what organic particulates you do catch in your filter floss or what have you eventually will break down anyways and its chemical products should be dealt with by the biological portion of the filter.
2.) Chemical filtration is completely superfluous in most cases. Sure carbon can be used to remove medications but that's a very rare circumstance. Most tanks do not need any form of chemical filtration at all. I haven't used carbon in any of my filters in about 5 years.
3.)Aeration isn't the function of a filter. Rarely have I seen anyone use a spray bar to move water at the surface. HOBs inherently cause surface agitation but the movement of gasses should be easily facilitated by the stagnant surface area of the water. It helps but isn't 100% necessary. A canister filter doesn't aerate the water like a HOB would...
More importantly is flow which I'll discuss next.
Biological filtration in my opinion is the single reason we have filters. The reason we have filters and don't just rely on the substrate for filtration is because there is little to no water movement in the substrate. Thus ammonia rich water won't be in contact with the bacteria and thus won't be reduced (technically oxidized) into a more friendly state. A filter may not substantially increase total surface area with in a tank but it
will increase bio-available surface area which is a combination of the density of bacterial growth and its effectiveness. Flow is a very strong factor in the balance of a tank. It keeps small particulate waste suspended in the water and forces water into and through the substrate and through the biomedia. You can't have a biologically balanced tank without flow. Often times freshwater aquarists fail to realize flow is as important in fw as in sw. You just need less of it.
So to sum things up:
No, you don't need a filter. A few power heads will do fine. However, you will not be able to stock your tank to maximum capacity. Maybe 1/3 of the fish you would be able to with a filter.
Even then you don't need power heads but again, expect to reduce your stocking levels significantly.
on a side note...yes protein films are disgusting but what can you do lol.
edit: nevermind I've used carbon just last month to clear up my tank after digging around the substrate.