Filtered water does indeed improve the taste of coffee and tea. I know it does of tea, which is more subtle and which I must drink at it’s optimum. Coffee which I drink more in the soup form, I cannot really discern by type of water. I naturally assume the two conform to the same principal.
First of all water quality is greatly determined by where you live. If you live in a hard water environment you can have bad and nasty water. Hard water has all kinds of dissolved minerals, which you may need to remove before you can even drink the water. Some people even have to neutralize their wash water just to wash their clothes.
Secondly mineral water is not good for tea. I know. I refuse to drink such dregs. When I’m under direct orders to be civil, I might decline all beverage. Alchemy will happen with tea and mineral water. The tea will darken to a sickly kind of black. It will taste horrible and rob you of all joy. Then you will become the living misery like me.
Though I am a very reasonable person, I will filter my water for tea. I am not the same about coffee, because my palette is not refined enough to distinguish the difference.
Carbon filters also take out some of the chlorine which is a volatile gas and toxic to many living things.
I have often been the generous host of some very fine people, due mostly to my loving and generous spouse. Some of those Neanderthals we take in have taken the spring water and put it in the kettle for tea. In such circumstance, I feel I know exactly how God feels about transgressors and sinners. I too go into the long suffering mode and mark it for future reference.
Filtered water does indeed improve tea. Here is how you can find out. Brew two cups of tea. Use filtered water in one cup and non filter water in the other. Take a third one if you have mineral water handy and make three cups. Brew them for the same amount of time. Do a subjective taste test.
You will immediately hate the mineral water tea. You will hate the color and loathe the taste. The filtered water will give you the pleasure you need but you will live in misery because you tasted the mineral water tea. The secret to happiness is obliquely revealed herein.