Why use the bootstrap for a skewed statistic when you can use a transform? Let's say you are working with a statistic (say, the mean of the population) of a skewed distribution with a long, long tail such that confidence intervals must be very skewed to achieve reasonable coverage precision for reasonably high n (<100) samples. You can't sample anymore because it costs too much.
OK, so you think you want to bootstrap.
But why?
Why not simply transform the sample using something like the Box-Cox transform (or similar)?
When would you absolutely choose one over the other or vice-versa? It's not clear to me how to strategize between the two.
In my case, I want to construct confidence intervals to make inferences about the population mean on a non-transformed scale. So I just assume I could transform, construct intervals, then reverse-transform and save myself the trouble with the bootstrap.
This obviously is not a popular choice. But why isn't it?

If you really mean that you want to transform the sampling distribution (as an earlier version of the question as well as comments indicated was the case), the main disadvantage of bootstrap is lost. In order to have a sampling distribution that you can transform, you have to create it. If you’re in the common situation where you do not know the population distribution and cannot analytically calculate the sampling distribution, then a way (and the only way I can think of) to get that sampling distribution would be to simulate it…
…by bootstrapping the original data, calculating the mean (or whatever) for each bootstrap sample, and getting a distribution that you can transform.
By bootstrapping anyway, you lose whatever computational advantage you hoped to have. Combine that with some arbitrary-ness in the transforming, and this sounds like a losing strategy.
