What good is an idealization? It seems to me that an idealization may serve two purposes: either it provides by itself a good enough approximation to reality for certain problems, or it can be easily combined with other idealizations to yield a useful picture of the world.Indeed. all theories in economics are, to some extent, idealizations. And no economic theory is all that good at predicting reality, at least not nearly as good as theories in the physical sciences.
One method I've brought from my study of the physical sciences is to be extremely conscious of your units of measure. Not only do you want to be rigorously consistent about your units, you want to know what your units mean. The meaning of a unit has two components: the operational definition: how precisely do you measure things in that unit, and the physical definition: what actually existing physical property of the object being measured corresponds to that unit. There are cases where scientists operate with units and quantities that aren't physical (such as with the ideal gas law), but by and large it's Very Important to assign a physical meaning to your units of measure.
Most of economics use some currency as the direct unit of measure. But currency by itself does not have any sort of physical referent. Indeed, because currency defines a relationship between quantities that (presumably) have the same underlying units of measure, a quantity qualified by currency is a dimensionless quantity: it has no units of measure. Dimensionless quantities are important in and of themselves, but it's also important to be able to talk about real physical things using real physical units of measure.
A labor theory of value gets us at least closer to thinking about economics using units of measure that directly reference a physical quantity: human time and effort. It doesn't get us all the way there, because of the "abstract" (subjective) and "socially necessary" (statistical) components of the definition. And a labor theory of value seems at least intuitively better than referencing the prices of specific commodities to tie prices to objective physical reality.
As far as understanding market prices is concerned, the labour theory of value does neither, since there is no theory of 'frictions' that can be added on to the theory to make it more realistic.Not all economists endorse the methodology of adding "frictions" to an ideal model to generate a predictive model.
But I'm not at all convinced that one can't add "frictions" to a labor theory of value. I haven't studied enough economics to offer a rigorous mathematical rebuttal, but in general replacing perfect rationality with an evolutionary model using uncorrelated heritable variation and natural selection seems to have considerable potential, giving us a mechanism that might result over time the equilibrium that perfectly rational people would figure out instantaneously.
To my mind the debate on the transformation problem shows that there is no meaningful connection between labour values and prices.I'm not yet convinced* that the transformation problem is (a) unsolved, (b) important at all or (c) a problem specifically for a labor theory of value. Marx seems to consider the transformation problem to make very specific predictions about capitalism; he does not seem to treat it directly as a way of connecting the LTV to observed prices in general. It's also worth noting that according to the Wikipedia article cited by the commenter, the transformation problem assumes that the use of capital requires not just compensation for its creation, but a continuing rate of return. This assumption might constitute an externality, which would require a specific kind of mathematical treatment. As I noted earlier, my understanding of mathematical economics is not yet sufficiently sophisticated to address the problem more rigorously.
When I use this particular phrase, it should be noted that I'm equally unconvinced of the opposite; I'm truly agnostic.
On the other hand the standard micro discussion of prices (or Sraffa's prices of production for those so inclines) is no more complex than the labour theory of value and much more convincing empirically.It would be nice to have a link to an authoritative description of these models; a superficial search of Wikipedia doesn't yield anything particularly illuminating.