The Gaussian copula is not an economic model, but it has been similarly misused and is similarly demonised. In broad terms, the Gaussian copula is a formula to map the approximate correlation between two variables. In the financial world it was used to express the relationship between two assets in a simple form. This was foolish. Even the relationship between debt and equity changes with the market conditions. Often it has a negative correlation, but other times it can be positive.
That does not mean it was useless. The Gaussian copula provided a convienent way to describe a relationship that held under particular conditions. But it was fed data that reflected a period when housing prices were not correlated to the extent that they turned out to be when the housing bubble popped. You can have the most complicated and complete model in the world to explain asset correlation, but if you calibrate it assuming housing prices won’t fall on a national level, the model cannot hedge you against that happening.