However there are significant tribological systems for which a minimum friction level is essential. In these cases, achieving a high-enough friction coefficient, often in spite of the presence of a lubricant, and in a stable manner (so NOT significantly reducing with run-in effects) can be a valid and essential goal.
Quite simply, there are some tribological interfaces that simply MUST operate as far to the left of the Stribeck curve as possible, whether that is viewed at the macro or micro scale.
Here are some examples. Can you add any more?
Brakes (pads - discs, or shoes - drums, etc)
Airport runways (tyre - runway surface)
Rolling bearings (roller - cup or cone)
Threaded fasteners (inner thread - outer thread)
Walking/running (shoes - the ground)
Railway traction (wheel - rail)
Traction drives, e.g. Torotrak
Clutch plates
It's interesting to think in each case how engineers have tried to maximise the friction coefficient, for example by carefully selecting materials, or including surface features to channel the lubricant film away from the contact patch.