Frequentist inference with Dirac delta as prior Would likelihood-based frequentist inference amount to the same as Bayesian inference, but where the "frequentist prior" $\pi^F(\theta) = \delta_{\theta^*}(\theta)$ with $\delta_{\theta^*}$ being the Dirac distribution centered at $\theta^*$?

Dirac delta prior would mean that posterior can only be the same as prior or undefined if prior is inconsistent with the likelihood. Posterior is
$$
p(\theta|X) \propto p(X|\theta) \, p(\theta)
$$
so with Dirac delta as a prior, it would zero out every value the prior is not centered on.
This is the opposite of the likelihoodist approach that uses only the likelihood, while with the Dirac delta  prior the result comes only from the prior.
