Yes, I think we agree. Except that i don't think that the fact that there is meaningful argument to be had about bayesian inference v.s. frequentist inference, means that the debate has not been centered around arguing about what probability is, which is a mistake; the same class of mistake as the mistake being made by the realists and idealists arguing over sound. The bayesian and the frequentist have proposed ways to settle their debate. And there are observations which act as evidence for bayesian inference, or frequentist inference. But exactly what experience should i expect if i think "probability is frequency" as opposed to if I think "probability is subjective degree of belief" ? Arguing about which inferences are optimal, is perfectly reasonable, but arguing about what thing probability really is, is silly.