Would you also say that "main body Physics" insists that a gas is a continuum because it uses the gas laws? Those gas laws came from the statistics of large numbers of discrete particles and we all live with that.But this is many-body physics! If you think you can, for example, derive the Fermi Liquid Theory via adding up such single interactions, then I want to see it.
The definition of a conductor here is that there is no gap at the Fermi level! Period!
Now, if you wish to argue that you can show that there is a "just finite" gap here, then I want an exact reference. It is that simple.
They are only models, remember.