The Labor Theory of Value is a mind projection fallacy. Value is something that can only exist in minds, and if everyone were to suddenly change their minds about that which is valuable, all the labor in the world used to produce a previously desired product wouldn't mean a thing. Marxists recognize this, which is why they talk about "socially necessary labor-time," a self-defeating addendum if there ever was one.

Huge pet peeve: you're eliding between separate concepts in Marxian political economy. "Use value" has the referent of what you're calling "value;" while "value" simpliciter refers to SNLT. Of course if prior demand is a sufficiently poor estimator of future demand then LTV ceases to be a useful simplification of reality, but that's an empirical question.