Given the discussion here: Why are p-values uniformly distributed under the null hypothesis?
And, particularly the point that @whuber brought up on the composite hypothesis (link here).
I'm wondering even if the distribution of p-values is not as good looking as it should, would it be fine to just empirically estimate the distribution of p-values (under null) or test statistics and calculate empirical FDR based on that?
So, this means that we can generalize this to all the cases where this happens?
Of course, it's always good to find the root of the problem. And, that this test is suffering from having Type I error less than selected $\alpha$. However, if one can get a good estimate of FDR by permutation on the expense of more computation, it's always a good idea, at least to me.