Which I consider superficial. The curves as a whole still look like sine waves, but scale along the curves is completely different in a manner that cannot be straightforwardly predicted from the shift to the curves themselves. Indeed, the plate carree isn't equal-area, so what Eckert VI is doing is combining an equal-area and non-equal-area projection, and then fudging the final results until they look equal-area again. In any case, the actual benefits of the sinusoidal projection are lost, as Eckert VI has neither a conformal equator or central meridian nor equally-spaced parallels, making there no discernable benefit to using sine waves over any other shape in this case.
Eckert V is less superficial, since it keeps the parallels at the same spacing, and so is an actual averaging of the sinusoidal and plate carree projections, and retains properties which both of those projections share. But it isn't equal-area.