My experience was that the tools are absolutely useful. Green Belts are those who learned the tools, but stayed at their day job. Black Belts are when you pivot into doing it full time.
Much like people who underperform in technical fields often pivot to Management, you see the same in the pivot to Process Improvement. That creates the issue of the lowest performers at the actual job being the ones most inclined to pivot into that position.
There are always good ones (I'm biased, but think I was). The issue is that they are a relative rarity due to those (and I'm sure other) factors.