your body signals that you're thirsty for a reason, ie: you need water. That's the mechanism to let you know that nature provided you.
Nature knows best, drink when you're thirsty *shrug*
2 litres of water a day, barring some medical need, is just odd. You CAN overhydrate, and you'll just pee out the extra normally anyway. Maybe people like peing 20 times a day, I don't know, that's none of my business.