These water discussions always amuse me, and find it funny how everyone becomes a chemist and expert.... while I am 100% sure that the water on board is completely safe for eating and drinking, otherwise I wouldn't go on board and eat or drink anything....that doesn't mean bottled water is a waste...
While you could go and refill a container from the beverage station, you would also need to clean that container throughout your cruise, otherwise that clean water wouldn't be so clean anymore from stuff in the air or some slight backwash so you'll probably need to carryon some cleaning agent, and something to clean it with. And find a place to clean it....You'll also need to store that cleaning instrument in a place that likewise can't get any airborne germs or other bacteria on it, taking up rather important space in your stateroom to dry everything out... Then what if you are a night drinker and need water at night, do you really want to run all the way out to the beverage station for some water, maybe you do what others have posted and refill from the bathroom, technically the same clean water, oh but wait while I'm confident in the food prep area and the beverage station, those pipes and water lines are probably cleaned out from time to time... The plumbing line in your bathroom ehhh I'm guessing not so much...
Look my point is that for those who drink a lot of water During the day, the convenience of being able to quickly grab a bottle of water at night or on your way out to an excursion is worth it or just a cold bottle out of the fridge on a hot carribean day works for some....And the alternative does require extra effort while you are on vacation where time is precious....and carrying all of those supplies needed like bottles and cleaners does take up space in your carryon and valuable shelf space in your bathroom, So before dismissing bottled water simply bc you feel the water tastes fine, that isn't the ONLY reason, for some it maybe and that's ok too....
We do take a case of water with us it works for us well and will do it again. Just don't put any liquids in your checked luggage.
Now if you insist on refilling water on board please for your own sake buy a refillable container don't just reuse empty disposable bottles they aren't intended to be used that way