Cycled water

There is a weird thing that comes up again and again, cycled water. I think it’s time to bust that particular myth wide open.
For a tank to be referred to as cycled any ammonia produced by the fish is converted into nitrates without harming the fish. This is done by archaea and bacteria.
The archaea and bacteria in question share one feature, they are photophobic and non motile, they hate light and they don’t move. Add to this they need to access ammonia and nitrite depending on the species, then they thrive in flow. That means the filter is the perfect place for them. The archaea and bacteria that dominate in the tank can not survive for very long at all in water.
This means that water either contains ammonia and/or nitrites, in which case the archaea and bacteria in the filter are not detoxifying the water, or it contains neither of these, the filter is doing it’s job.
The water has nothing to do with getting rid of the ammonia and nitrite.
Does this mean you can change 100% of the water and all will be well? Yes, and maybe.
This maybe is because the water in your tank may not be the same parameters, chiefly pH, KH, and GH, which may not match that coming out of your tap. As ammonia is converted to nitrates the water will become more acidic. As ammonia NH3 becomes Nitrite NO2 the hydrogen ions, the H bit of NH3, is released, and that is what makes acidic stuff, acidic. A lower pH, anything less than pH 7, is acidic, and all that means is there are H+ ions.
As H+ ions go into the water they will react with carbonate molecules, the KH, causing that to drop.
What this all means is that in a tank with a functioning filter, the archaea and bacteria will cause the KH, and then the pH, to drop. If you do large regular water changes then that isn’t going to be an issue unless you live in a very soft water area.
Add to that some of us have variable water out of the tap. As supplies change, or just rivers dropping or flooding the water we get in our homes may be slightly different.
Let’s say someone moves their fish from one tank to another, and uses 100% new tap water; If they have been doing regular water changes the water parameters will be similar and the fish can move straight over. If the tank maintenance has been insufficient to keep the tank kH matching the tap the fish will struggle and some may die. If they had allowed their pH in the original tank to drop below 6 at which point most of the archaea and bacteria have died, and when the filter is moved over the fish are put into stressful conditions and may well die. That is probably why the myth of cycled water has come about.