For almost all the typical use cases a Frequentist 95% confidence interval will be nearly the same as a Bayesian 95% credible interval determined using a unifor

For almost all the typical use cases a Frequentist 95% confidence interval will be nearly the same as a Bayesian 95% credible interval determined using a uniform prior. In every case I have seen where this is not true the Frequentist interval gives nonsensical results. So your complaint is a total non-issue. Most people are interpreting their confidence intervals as credible intervals anyway... Essentially, for nearly a hundred years researchers have already been using Bayesian stats with flat priors.