I think you have to remember that things like 6-sigma, TOC, and Lean are not designed for expert practitioners like IEs, statisticians, operations researchers, etc.
At their best, they take people like line workers, supervisors, and managers, with anything from a high school education to maybe a BA in Business... and give them some basic mathematical tools for trying to run their business operations better. At least "better than nothing". They use some big simplifying assumptions and provide some easy-to-remember rules of thumb for running better processes.
At their worst, they're pseudo-science being peddled to unsuspecting companies for vast sums of money. But even so, they are probably not causing too much actual harm.
But also consider that while you've spent thousands of hours in training to become an IE, these programs are designed to instill the most basic but essential bits of information - probably within 40 hours of training... to people with no statistical background.
Think of all the people who aren't in your program that have no idea what a sample size is and have never even thought the idea "how many times do I need to try this before I feel confident in my results".
It's a lot like taking first-aid classes. Doctors have over a decade of education to do what they do. A first-aid/CPR class gives you some essential life-saving nuggets of information that are completely un-nuanced and memorized... in less than 8 hours of training. The knowledge from that first-aid class is important and helpful and certainly better than not having it. But on the hand, the risk is thinking you know more than you really do.
Lastly, what you're uncovering here is the true ugly truth in business... that so many people are operating at such a vast level of ignorance that even the most basic math and science tools yield huge benefits. At my last company, the forecasting process was so bad that even applying a simple moving-average forecast often gave far better results. In such environments, even these possibly shady programs like 6-Sigma, Lean, etc., yield benefits.
Lastly, the smart move for you would be to go and create a new program based on IE principles and get businesses to buy it. Print and bind some slick-looking training materials and diplomas at Kinkos and you'll be rolling in the dough!
And clearly I haven't had enough to drink.