My tap water is terrible and I switched to drinking distilled water a long time ago, making tea with it, too. I know everybody says it makes tea taste flat, but it's been tasting fresh and crisp to me.
While in LA this past spring, where the water is even worse, I got tired of looking for water and paying deposits for the containers. I switched to refilling my gallon jugs from a 25-cent RO machine. After a while of doing that, I got tired of lugging the jugs downstairs and up again and bought a Brita filtering pitcher.
About two weeks ago, I went back to distilled water out of curiosity. I'm supposed to change my filter, soon, and I wanted to see if I could tell the difference with tea made with distilled water and water made from the old filter and new filter. Distilled water stills gives me that fresh, crisp sensation and on a whim, I bought a bottle of spring water.
Wow, what a difference! Yes, distilled water gives a distinctly flat sensation to my tea while spring water gives a very nice, soft, rounded feeling.
Unfortunately, my next bottle of spring water came from a different store and the spring is in a different state. The difference isn't as remarkable and I don't like it as much. It might be because the water wasn't processed the same.
So, now I get to be a connoisseur of spring waters as well as of teas and brewing methods to get the most from the experience.