quantile regression is computationally intensive and inverse transformations usually less so. Although you could certainly make the case that, given enough data, quantile regression better captures what we actually want to find, most of the time (i.e. how's this effect diverge towards the extremes).

Normit typically (not sure if universally) has the lovely property of giving you something like a marginal t-test without the assumptions of mixture-of-gaussians errors. You don't jerk around with U-statistics and thus the sample size doesn't make the test statistics so damned granular.