What exactly is antiquated about the design of modern water fountains? How could the designers of the water fountain effectively and reasonably communicate that the water fountain is safe to drink from, and do so for the design life of the fixture?
Sure, some water fountains look old...but I imagine that if you live in a major city, odds are (from a logistical standpoint, unless you live in a new subdivision) the tap water to your house or apartment flows through pipes that are older than that water fountain. A dog drinking from the fountain is gross, but I'm not sure the onus is on the designer to totally prevent people from acting silly.
Good design can always find a solution -- off the top of my head, integrating some kind of sterile recyclable mouthpiece dispenser would assuage most concerns
In the case of potable water valves, this is accomplished by preventing backflow and being made out of a hard smooth material. When you turn on a drinking fountain, the stream of water flushes any loose dirt and debris, so as long as you avoid contact with the fountain (the stream should be adjusted so that this is easy), there isn't going to be significant transfer of anything.
The design is not antiquated; actually it's pretty brilliant. However, if the water pressure is insufficient, the main protection doesn't work. And that's distressingly common.
Nine times out of ten, when I go to a water fountain, it's barely a trickle, so I'd have to put my mouth right on the spout to get any water. After this happening a number of times, you sort of give up after a while.
The burden of proof is on the water fountain (or more specifically, the designers of the water fountain) as to whether drinking from it is safe.
This is not a problem with being overly cautious. This is a problem with an antiquated design.