Direct Comparison Between A Protein Folding Hp Lattice Model And A Real Protein Structure?

Question

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I have been recently reading a lot about protein lattice models and how they try to predict protein structure. There are really many papers on this subject, but it seems incredible to me that I have not seen any "direct" comparison between the lattice alpha-carbon prediction of the protein structure and the crystallographic structure for some proteins, so my questions here is;

Has anyone ever seen a direct comparison between a protein folding HP lattice model and a real protein structure (PDB)?

If not, I would think that such models are totally useless, so why so many papers about the subject?