In India, water is much more of a shared public resource. Playing basketball on the public courts, if you bring a bottle of water, you should expect to be asked to share with anyone who wants a bit.
This is a public water source. In most places I’ve visited, a drinking fountain is the dispenser of choice. Here, a shared cup is the option.
I think that using a cup would tend to reduce the overall wasted water, since you’d tend to drink it in quantized amounts. As opposed to the drinking fountain, where you have a constant flow, some of which one invariably fails to consume. However, the added number of parts required, dust and dirt, potential cross-contamination and other factors tend to make me favor the drinking fountain.
I do not know why the chains were made long enough for the cups to fall to the ground. Potentially to allow for the cups to be raised up enough to reach a taller person’s mouth.