I like KT because it rapidly eliminates ambiguity and creates packages of information that can be passed seamlessly between teams or stages in a workflow. There's little or no rework in a KT shop, and few "pipeline stalls" where someone is blocked because a decision hasn't been made or communicated, or because a dependency is discovered too late. I learned it at a company I was at about 10 years ago, there was one guy who had used it in his previous job and he convinced senior management, and so we were all sent to KT for their training course.

If you want to get a flavour of it the original book is pretty cheap now https://www.amazon.co.uk/Rational-Manager-Charles-Higgins-Ke...

Like I say I've tried 'em all, well nearly, KT is the only one that's worth a damn. Even the simple exercises like "is, is-not" make you feel like Poirot.

Based on the description at the link, Kepner-Tregoe analysis looks like a useful and light framework for eliciting and applying critical thinking in project management. But the key words are "critical thinking." The principles of the agile manifesto when put in practice by people who have domain knowledge and who have aptitude for critical thinking confer on a project a good chance of success.

Those kinds of projects and teams have that edge over others because they have critical thinking on their side. That will benefit them first in seeing that they don't need to add a large, trademarked, expensively trained process around agile, and subsequently in remaining focused on people and code rather than process.

Tangentially related, I recommend learning and getting certified in Lean Six Sigma. It's PM * stats * MBA. The systems analysis / theory of constraints perspective also completely explains why agile falls short in the face of external road blocks.