Certainly you would not be the first to have a lightly populated tank w/o a filter. Your gravel has a LOT of surface area. That is significant in that that is where most of the beneficial bacteria (the ones converting ammonia to nitrites and nitrites to nitrates) are operating.

The water has relatively few bacteria. The tank walls probably have more.

What an effective biological filter has is yet more surfaces for the "good-guy" bacteria. Then the flow of the water bring oxygen by the surface even more quickly to those surfaces and the gravel and the tank walls and other structure.

Most new aquarists don't understand or, sadly, haven't even heard of the Nitrogen Cycle. (You guessed it - look in immediate help.) It takes a month and a half to two months to establish and then only if we don't overpopulate the tank or clean out the gravel or filter media so vigorously that we wash away or dry out the good-guy bacteria.

Until it is established, we have no business adding new fish!

Decorations, plants, other aquarium accessories even, add "surface" to that process. That is why an inch of gravel is superior to a light cover of it - though deeper gravel may not circulate much water through it and offer a lot more "living surface."

Of course when we add some plants, if lit, they will directly absorb and use some of the ammonia in the water. That is a dimension often overlooked.

This is a little gross but with those guppies cheerfully eating all that you give them, they must then pass some urine (largely ammonia) and feces (with a lot of ammonia). After all, "poop happens." So in a very real way the fish are swimming in their toilet. That is where weekly partial water changes come in.

"The solution to pollution is dilution!"

Or as Dr. Charles Harrison once, exasperatedly replied to a guy who could see no point in water changes, "If you have a dirty toilet, how do you clean it?"

So you aren't a mad scientist. Maybe a little angry... ;)

I look forward to your answers to the questions in the first paragraph.