> the frequentist concept of confidence distribution is gaining acceptance, which is the proper frequentist equivalent of the posterior, so this distinction between Bayesian and Frequentist is disappearing

The major distinction remains: Frequentist confidence intervals are something quite different from Bayesian credible intervals. I don't think that having a distribution that can be used to calculate any desired confidence interval - like the posterior distribution can be used to calculate different credible intervals - changes much.