indicated. You aren't mixing the pigments between the leather and the polish like you would when mixing paint or clay. You are putting a transparent color over an opaque color. When applying a darker transparent color over a lighter base, the outer layer absorbs more and reflects less light than the leather underneath it, while some light still passes through and allows the original characteristics of the leather to reflect what is left. However, it simply doesn't work when a lighter transparent color is put on a darker base. Because the outer coat is absorbing less light than the leather underneath it, it simply isn't doing anything while still transparent. The permanent pigment (edit: of the leather) can never be made to absorb less and reflect more light than it did unless it is blotted out with pure wax, which has no characteristics of leather. It would look like a flat chili colored mess of wax instead of leather. Think about painting over a wall. The pigments don't mix if the paint was dry, and it would take many coats of a transparent pink to overcome a dark red, while it would only take one coat in the other direction.
If we're talking 'instant' results then, yes, stripping and re-dyeing is the only way to go from a dark to light shade. If you have a longer (i.e. years) timeline, using the lighter polish is not superfluous. Here is a pic my 'old' chili Delray next to dark chili:
I allowed them to lighten by mixing applications of chili shoe cream with walnut, mid tan and even neutral cream and wax. I also used some dark brown and black on the burnishing. I'm currently doing something similar with my dark chili Bleecker Street. It will probably be a couple years before I even notice anything and another few years before they settle into the desired shade.