Permutation tests don't account for family-wise error rate effects, so I'm curious why you would say that "it doesn't overcorrect like traditional methods".

I'm also curious why you say those "cover every case", because permutation tests tend to be underpowered, and also tend to be cumbersome when it comes to constructing confidence intervals of statistics, compared to something like the bootstrap.

Don't get me wrong -- I like permutation tests, especially for their versatility, but as one tool out of a bunch of methods.