Really? I thought it was just British people being old fashioned or lazy builders.
It's a matter of aesthetics and personal choice as much as anything else. I prefer having two taps. No fun pouring a glass of squash with the first glug being warm water left behind in the tap; similarly pointless wasting half a cup for the sake of waiting for it to cool down.
I won't drink out of any tap - home, work, train, otherwise, that isn't marked as drinking water or that I know is safe. Using water in conjunction with soap to clean your hands after a widdle is one thing. Consuming it is another. I've had some serious stomach cramps after drinking slightly off water before now.
Any on-train-caterer worth their salt should offer water for tablets - if not the whole bottle then certainly a cupful, enough to take the tablet but not so much that they're essentially getting a free drink. Same with hot water for Lemsip etc. Some even offer it for babies' milk. I think if you make a reasonable request explaining your needs you should be accommodated, as opposed to marching up to a buffet or trolley and demanding, shouting about rights and quoting legislation etc.
Of course there will be circumstances where it's not possible... for example some trolleys have the exact number of heat-proof cups for the total possible drinks on their trolley, for example and must account for them all at the end of trade; thus they will have been told by their bosses that they cannot accommodate such requests. Similarly trolleys with hot water pots, as opposed to freshly drawn water from a boiler, may not be ideal for babies' formula.
It's a train at the end of the day, not a Pizza Hut or a Starbucks. It'll be able to do some things, and other things you must not expect or demand entitlement.