Yes, exactly! This is essential.

I'm assuming you're using some moral sense of "value" here. But this is exactly the famous "water vs diamonds" thing.

Water is essential for life. Its true utility to humans is incredibly high. If there is, for whatever reason, a shortage of water, there is basically no limit to how much labor or money we would be willing to trade for it. Price follows utility for human survival in cases where there is any pressure. Marginal utility handles this case without skipping a beat. LTV basically can't handle it without going outside the theory.

Marx spends some time in Capital talking about changing means of production. But if you have something stockpiled, even his analysis concludes that there is a mismatch between socially necessary labor and price, because the labor and price aren't synchronized in time.

As a moral argument, that labor is important because people are important and they imbue that importance into everything they do. But they don't only attach importance to things that have prices attached. So LTV is also badly defective as a moral theory, as it is completely okay with sacrificing non-monetized importance (including, for example, the lives of non-laborers!). Marginal utility also is badly defective here as it treats these things as levers to exploit people with. But in a way it's actually morally more justifiable than LTV because you say: people matter, and what they value matters, and you know how much because they tell you via how much they're willing to pay for things. In contrast, LTV establishes the idea of "labor" as a proxy, thinking that it knows better than people themselves what is important to them.