It's crucial for the transformation because it works as the real convincer. That brings credibility, and credibility brings participation. Responsiveness makes this commitment visible. The emphasis on internal response and internal training is deliberate. It's not unheard of for consultants to come in, recommend changes, present a bill and leave.
Temporary improvements happen, but soon enough the old status quo is back.
The deepest and strongest kind of change is internal and homegrown. Naturally, on-time delivery, unit cost and other measures are poor in the first round, and participants are thoroughly disgusted. But soon they're actively improving their process, with coaching in lean techniques from the facilitators. It gives the participants a real taste of what it's like to work in a lean environment. One is using production-style components to make a functioning product that can be tested.