A really, really stupid strategy can still meet the requirements for being a Nash equilibrium, because a strategy being a Nash equilibrium only requires that no one player can get a better result for themselves when only that player is allowed to change strategies.
A game can have more than one Nash equilibrium, and a game with more than one Nash equilibrium can have one that’s arbitrarily worse than another.
Two (related) morals of the story:
A really, really stupid strategy can still meet the requirements for being a Nash equilibrium, because a strategy being a Nash equilibrium only requires that no one player can get a better result for themselves when only that player is allowed to change strategies.
A game can have more than one Nash equilibrium, and a game with more than one Nash equilibrium can have one that’s arbitrarily worse than another.