[RPG] What’s the point of quivers

A ration weighs two pounds, but a character only needs to consume one pound (half a ration) per day.

The key word in this case is need and how this is very different from should. A character, at a bare minimum, needs be consuming one pound of food per day, but very rarely will anyone want to get by on the bare minimum amount of food unless it's a survival scenario and resources are scarce. It stands to reason that a ration is two pounds because consuming a whole ration would be enough food to comfortably satisfy a day's requirement of food, and therefore, what a character should consume per day.

We can very easily reword the quote to yield the following:

A character needs one pound of food per day and can make a ration last longer by subsisting on half rations. Each half a pound of food, or quarter of a ration, in a day counts as half a day without food.

The word subsisting supports this interpretation because of the following definition provided by a simple Google search:

subsist - maintain or support oneself, especially at a minimal level.

It could stand to argue that if a ration were intended to be one pound, one could not, by definition, subsist on half a ration by definition since half a pound of food is less than what is required in a day.

If that's the case, why shouldn't I only consume half rations to save resources?

As mxyzplk mentions in his comment,

real people, unlike computer game characters, don't like subsisting on EXACTLY THE MINIMUM AMOUNT TO LIVE EVERY DAY.

We must remember that rations are intended to sustain adventures and travelers who will very likely need more than the bare minimum amount of food daily. If we consider modern body builders, they can very easily consume six meals a day as opposed to the average three because they must sustain their added muscle mass. One might be able to argue that a warrior might need more food than a wizard, but neither will be happy if they only ate only what they needed for an extended period of time.

This, unfortunately, does not offer a mechanical reason as to why a character should consume more than a pound of food a day and I am unaware of any in-game rules which address this either. This would suggest two possible solutions to encourage players to consume a full ration whenever possible:

1. Reward players who consume a full ration (or a large enough meal) with a temporary buff. This is a result of the character being well fed and ready to address any challenges they may face.
2. Penalize players who are attempting to live off of the bare minimum. In this case, you can easily apply any penalties which a hungry character suffers, but to a lesser degree to seem fair.

As to which should be used and to what degree is up to the GM's discretion for what they believe is a best fit for their campaign or scenario.

What makes you think that a well or stream costs money to use, by default? The DM is able create any sort of water monopoly he likes, but in general streams, wells, and lakes are plentiful and unguarded. DnD has a history of heavily implying that while Ale costs money at an Inn, the water is free.

As for its weight. When it is not explicitly discussed, 5th edition DnD mechanics are assumed to emulate real-world mechanics, such as the density of molecules and the laws of physics. So Water weighs approximately 8 lbs per gallon. This works out very neatly with the stated weight of a full waterskin, which would then be 1 pound for the skin and 4 for the water.