If the number of dimensions is high enough then pretty much all points are far away from each other so there's no real need to worry about points clustering. You're at a much greater risk of simply missing interesting parts of your space than you are of oversampling any part of it.

This can be especially bad if one corner hides a catastrophe. Any automatic method is likely to have an exponential struggle to sample appropriately. At a certain point, you just need to apply your own understanding of the problem you are trying to solve, and resort to an ad hoc method to do the “right” thing.

That's exactly the problem QMC methods solve. By choosing a sequence of sample points of low discrepancy, you make sure to sample the entire space as evenly as possible.

It does but if you've got 100s of dimensions then you have no hope of ever sampling anything close to the entire space. Even if you just pick 2 points per dimension you've got no way of trying every combination.

Just a guess, but if you think about Sobol sequences, maybe the available dimensions get exhausted in this use case and then QMC doesn't perform well anymore.