I need to look at my copy of Das Kapital again, but:

1. Doesn't labor measure commodities, and isn't it an average taking into account all labor in society -- not just the value of this particular productive act, i.e., cutting hair? I seem to remember that labor is necessary as a standard of value because without it, the various commodities are essentially incommensurable, making comparison (and thus exchange) impossible. That is, if I exchange x amount of grain for y amount of coal, I am presuming that there exists some third medium to which they can both be compared. This cannot be demand solely, because "keeps me warm in the winter" and "keeps me fed" are themselves incommensurable categories; how much "fed" is a "warm" worth?

2. Marx does consider demand, in the form of social use-value. Something cannot be a commodity if does not have social use-value; that is, a commodity is a complex of labor value and social use-value. For instance, I can spend five hours making the most beautiful mud pie you have ever seen, but it will not be a commodity, because mud pies have no social use-value. As a consequence, the labor spent making it will not produce value.

3. The water-in-the-desert example relates to productivity, which describes the the amount of labor which must be expended to extract or produce a commodity. Since water is hard to get in the desert -- one must either dig deep for it, or have tankers bring it in -- the bucket of water has a high labor-value. Note, again, that its labor-value has to do with comparison to other commodities within the total structure of an economy, and is not the sole creator of value in the bucket of water; if there were no economy, the water would still have use-value, because humans need water to live. Labor-value is thus more abstract than use-value, and is to some extent added over and above it.

4. Converse to #2, above; something can have use-value and yet not be a commodity. The example Marx uses is food grown to support oneself. The work involved in raising a family falls under a similar head, because a family is not a commodity; it belongs in the purely human sphere, which predates and exists outside of commodities. A parent's labor only becomes measurable as labor-value when the family itself becomes commodified, made abstract rather than concrete. For Marx, the way in which purely human things -- love, sex, family, etc., -- are commodified and made abstract is a prime example of the inherent anti-human nature of capital.