Hasn't Selfish Mining proved that Longest Chain Wins is not a Nash equilibrium?
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No. Because anyone who has greater than 33% of the hashrate must employ the Selfish Mining as their optimum strategy and everyone else must mine on the visible longest chains as theirs.

The Nash equilibrium does have a long-term failure as economies-of-scale centralization, but that is an orthogonal issue.

The problem with a DAG is no one can know the optimum strategy of the other participants and even which strategy they employed. Or at least not until you can show mathematically that no other strategies than following the Monte Carlo is profitable. The Monte Carlo is only the most profitable IF everyone else is also following it. That conditional "IF" doesn't apply in the LCR. That is the key distinction that makes a DAG fatally flawed.
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I was under the assumption that is miners had over 33% of the hashrate this would be the case.

I would also agree that DAG is flawed.

Lets say one was to mathematically work out the strategy even if they were deployed to what detriment would that pose to the rest of the miners?