Done correctly, you choose words (uniformly) randomly from some dictionary, so the best a model can do is predict that all words from the dictionary are equally

Done correctly, you choose words (uniformly) randomly from some dictionary, so the best a model can do is predict that all words from the dictionary are equally likely. All a model does is approximate probabilitly distributions, but the distribution isn't a secret; it's uniform. The dictionary doesn't need to be a secret either. The strength comes from the dictionary size and number of words.