I agree in the benefit of routine partial water changes to dilute pollution and maintain a healthy water chemistry. This is how nature renews fresh water with rain. I also wish to point out to any newcomers to the hobby that not doing partial water changes weekly may be the short path to failure and fish loss
However, at least in part, I feel I need to take the middle of the road here.
I'm remembering my youth in the 60's and my mothers tank. She had a 5 gallon, tar sealed, slate bottom Metaframe tank. It had an incandescent tube light in the hood, a bubble up filter with carbon and floss, just enough gravel to cover the bottom. She always had floating plants (Anacharis I think) and there was always a layer of mulm on the bottom. She had a catfish (emerald cory), an anglefish, a pair of red velvet swordtails, some other fish I forget and a (mystery like) snail.
She topped off the tank for evaporation, but never did water changes. The fish in this tank seemed crowded, but were big and healthy and thrived for years.
Not all tanks are created equally. First lets consider or rule out the newer tank not yet cycled and the tanks newer than 6 months not yet established. Weekly water changes in these tanks is even more crucial. Now lets consider smaller tank, the unplanted tank, the over stocked tank, the overfed and/or the poorly maintained tank...
Compare these to the larger, well filtered, heavily planted tanks with a modest stock level.
Or just compare alone the very small tank to the very large tank.
There are so very many variables that affect water quality.
Consider for a moment the commercial aquariums with thousands or millions of gallons of water. Surely they do not do 50% weekly water changes...but they have very sophisticated ($$$) filtration and additive systems that purify and regenerate the water (ensuring sufficient minerals and trace elements).
At the end of the day, the volume and/or frequency of REQUIRED routine partial water changes must be relative to any untreated pollution in the water. In addition, we must replace used nutrients and trace elements lost to fish osmosis and plant usage.
In a larger, well filtered, well planted, established tank, with a modest stock level, this may only be a few gallons a week. In a small, unplanted, overstocked and/or overfed tank, this may mean up to 50% twice a week!
I find myself in a somewhat unique and poor situation with very high nitrates (60-80ppm) in my (country) home well water system. This is most likely the result of a 95 acre farmers field across the road that gets ample amounts of organic (manure) and chemical fertilizer. Larger water changes are simply counter productive for me.
I've experimented with many things to deal with high nitrates and better purify water and plan to write these experiments and experiences in a separate article. However, boiled all down, my greatest success has been tweaking filtration for greater water purity, adding more plants, using additives modestly and reducing weekly water changes to 5g in my 60g tank or about 8.3%.
This has been working for me, with crystal clear water for many, many months now and I believe it will continue to be even more successful into the future.
Finally, some have suggested that the aquarium is a closed system that can't be managed as well as nature. Although I agree that we may be missing some key life forms that would [even] better purify water, we also don't have torrential rains that that muddy the water or runoff from agriculture, landfills and chemical plants, etc. Instead, we have a lab experiment where we can control the inputs and strive for very pure, healthy water chemistry.
Disclaimer: For the average aquarium, in addition to sound tank/filter maintenance and proper feeding, I simply must recommend a 25% to 50% weekly water change as the best way to ensure a healthy, consistent water chemistry for your fish.
If you don't manage the litter box, the cat is gonna pee on the sofa!