As I write in my edit, I do not know what the word “value” really means, so but if we replace it with utility, then we see that we pay prices based on the options we have, not based on the utility it gives us.

For example, paying $0.02 per gallon for clean, potable water, which surely one can agree has extremely high utility since it allows us to survive. But also paying $100 for a Christmas tree, which has lower utility. This is because we can get water for cheaper and the lowest price for the Christmas tree we could find was $100, but if water stopped being available for $0.02, then you bet people would pay $100 and even $1,000 for a gallon of water.

Does that mean water started having more utility? Not according to the definition economics used. Whether or not water became more valuable depends on how you are using the word value, so that is why I think it is not really a good word for discussions of how prices are determined.

You can sell a service to a business that is crucial to their continued operations all day long, but if someone else is willing to sell to them for less, then do not expect to get paid based on how “valuable” you are to the buyer.

I think economists use the concept of "marginal utility" to solve the problem you describe. If you already had 10 glasses of water, the marginal utility of having another drink is very low. If you haven't had anything to drink for two days, the marginal utility is high.

Your own example should make it obvious that "utility" is not a good way to think about value. Should people pay 100$ per glass of water, even if they live next to a river of fresh water? It wouldn't lead to good economic results to set prices that way.

I think anything else than "what people are willing to pay" will ultimately lead to bad results. For example the misguided "value theory of labor" keeps messing things up and leading people down the destructive path to communism.