Could reduced-lift wingtips allow an airplane to generate less wake turbulence?
Lift already does taper off gradually towards the tips, even on rectangular wings without any washout. That effect becomes stronger with tapered wings, of course. The reason is the pressure equalization resulting from flow around the wingtips, like you show in the lower picture. And like in that picture, the wake is spread over span in reality. Your upper picture is unrealistic and a gross oversimplification.

However, the eventual strength of the wing wake will be little affected by this. The resulting vortices are caused by wake rollup and do not come directly from the tips. The tip vortices are only a small part of the overall wake.

Regarding efficiency: Tapering lift towards the tips will make the wing more efficient. Lift far away from the wing root causes high root bending moments and requires a heavier structure. Lift near the root costs less structural weight and the net lift of the wing (lift minus wing weight) will be higher with a near-triangular lift distribution. This insight was published as early as 1933 by Ludwig Prandtl and rediscovered by R. T. Jones in 1950.