Bayesian analysis used merely as a computational tool? I have sometimes seen some statisticians used bayesian analysis and related techniques such as MCMC simply as a tool when a frequentist approach is not satisfying, typically for example when the maximum likelihood estimator is hard to find or takes too much time to compute.
In these case they focus only on the definition of the model and estimation (by MCMC for example) and barely on the choice prior distributions (from what I've seen).
I guess they use flat distributions by default but the particular choice of a prior is never discussed, maybe because of the large number of parameters the model may have and the difficulty to assign a meaningful prior distribution to each one of them.
Is it something usual to switch to a bayesian analysis and use it merely a as computational counterpart of a frequentist approach when the latter performs poorly?
My feeling is that bayesian and frequentist are very distinct statistical framework (at least that's what my teachers taught me!) and using one or another shouldn't be justified simply by computational purposes and moreover the choice of the prior distributions should at least be carefully made.
I know this is not really a statistical question but I just would like to know what pure bayesians think about this kind of use of bayesian analysis. Sorry in advance if it does not fit this site.

Comment: Here are a few reasons why a frequentist statistician might use a Bayesian approach.
Computational convenience, as @Fiodor1234 says, may not be high on the list.
One such example might be use of the Jeffreys posterior probability interval as a confidence interval for a binomial proportion. For example, if you have $x = 42$ successes in $n=100$ trials, the asymptotic Wald interval is not the best
choice because of the small sample size. The Agresti-Coull interval is easy to compute and comes close to more accurate intervals that are somewhat intricate to compute. The Jeffreys interval, based on the noninformative Bayesian prior $\mathsf{Beta}(.5, .5)$, is easy to compute in R and has good frequentist properties.
p.hat = 42/100
CI.Wald = p.hat + qnorm(c(.025,.975))*sqrt(p.hat*(1-p.hat)/100)
round(CI.Wald,4)
[1] 0.3233 0.5167

p.est = (42+2)/(100+4)
CI.Agr = p.est + qnorm(c(.025,.975))*sqrt(p.est*(1-p.est)/104)
round(CI.Agr,4)
[1] 0.3281 0.5180

CI.Jeff = qbeta(c(.025,.975), 42+.5, 100-42+.5)
round(CI.Jeff,4)
[1] 0.3267 0.5179

Proper support of distribution. In an attempt to find
the prevalence of a disease from screening test data, traditional methods can give an interval for prevalence
that extends beyond $(0,1).$ By using a Gibbs sampler with a beta prior distribution, it is possible to get a useful
interval estimate for prevalence. (Since the beta prior has the unit interval as support, then the posterior distribution will also.) See example..
'Simulate' latent data. Sometimes one wants to test or to give
a parameter estimate for latent data, which can be reliably reconstructed using a Gibbs sampler. One simple example is to know the variability of groups in a one-way random-effects ANOVA. Observed values from the groups are available, but the components of variance due to the various groups (separate from overall variance) are typically latent.
