There are established theories of probability that have nothing to do with ergodicity. See for example: Laplace - Théorie analytique des probabilités - 1812 K

There are established theories of probability that have nothing to do with ergodicity. See for example: Laplace - Théorie analytique des probabilités - 1812 Keynes - A Treatise on Probability - 1921 Jeffreys - Theory of Probability - 1939 Savage - The Foundations of Statistics - 1954 de Finetti - Teoria delle Probabilità - 1970