The Contradiction Between "Polygenic" Traits and High Heritablity

When I was critiquing genetic linkage studies back in the day, almost all of the studies would include something in the abstract about the trait they were looking at (intelligence, schizophrenia, depression, etc.) being “highly heritable,” as if this somehow lent credence to the results of the study.  After repeated failures to replicate, a new view of the genetic bases of of these disorders began to emerge and is now quite popular and accepted as a given by most scientists in the field, as far as I can tell.  I think it is best exemplified by a quote from this piece:

“Complex traits are just that—complex. Most traits are incredibly polygenic, likely involving tens of thousands of loci. These loci will act via a vast number of pathways”.

This idea isn't really based on anything found in the studies being performed.  Instead it was based on their failure, or lack of success at finding single genes responsible for these traits.  The thinking went, “since we can’t seem to find any specific genes responsible for these traits/disorders, there must be a very small effect from several genes working  together.”  The assumption that the trait was genetic in nature wasn’t ever questioned.  

As I see it, there is an inherent contradiction in this assumption:  The more genes involved in the expression of a phenotype, the less you would expect genetic heritability.  

To illustrate my point, let’s start with a basic Mendelian model.  Suppose that there was one gene for schizophrenia and to make it even more heritable, that gene is autosomal dominant.   If my 10th grade biology is still intact, that would give us a 50% heritability for schizophrenia in offspring.  Now, suppose there are two genes necessary to convey schizophrenia (and we will keep them both autosomal dominant for simplicity).  Heritability now drops to 25%.  A third gene would drop it to 12.5%, etc. Six or seven genes would drop it down below the actual prevalence of schizophrenia in the community.  

This, of course, is an  oversimplification, as you could have interactions between the genes, and all kinds of factors involved in whether the schizophrenia phenotype is expressed.  However, it seems quite clear that the more genes involved in the process, the more watered down your heritability would become.  It is hard to even imagine a scenario in which “tens of thousands of loci” contributing to a trait could lead to significant heritability, when offspring would get thousands of different genes from their other parent.  Leaving aside the mechanism of such a process, I challenge anyone to create a meta-Mendelian mathematical model in which tens of thousands of genes for a trait could convey a high level of heritability.  I’m not asking that you work out a model for a specific disorder.  Simply demonstrate how it would even be mathematically possible.  If you can’t do that, you have to ask yourself why you are holding onto the polygenic theory.