Water onboard the ship (served at meals, meals prepared with it, from the drink station, from the tap in your room) is all processed just like most bottled water (reverse osmosis and filtered).
A lot of folks don't care about the water taste or smell - and many can't even tell the difference. To us, water is our most important daily drink, and we consume lots of it to keep a healthy lifestyle. To that end, the taste makes you consume more of your favorite drink. Tasteless or "flat" water is one of the key reasons why many don't drink as much as they should.
Now, for the water on board:
1. Ship water is heavily chlorinated. As you know, it's sourced either from the port-side bunkers (after which it has to be quarantined for 24-48 hours first) or from seawater with reverse osmosis/distillation/etc. Minerals are added back if distilled, and chlorination follows. Those of us used to our favorite water source will find the end result either lacking entirely in taste or with a distasteful residue.
Bottled water is almost never chlorinated and is sanitized using ozone and UV light, neither of which leaves any kind of taste residue. Filtration/Reverse osmosis may still follow. If you are used to a particular bottled water brand, the water on board will taste VERY different.
2. While a ship isn't Flint, many are just not comfortable drinking water coming through miles and miles of ship pipes. Most ships aren't subject to stricter North American plumbing codes today - and keep getting drydocked without anyone touching their decades-old plumbing systems. This isn't to say ship pipes are subject to more corrosion - but it does bring up the need for caution.
3. Not all water bottlers are made the same when it comes to using recycled materials. Evian, for instance, will be in closed-loop manufacturing by 2025 - meaning 100% use of
own recycled plastic:
https://www.waste360.com/plastics/evian-use-100-recycled-plastic-all-water-bottles.