There is no "common wisdom" on this question, since many of the paid-by-the-word experts disagree.
The wrapper is the only part of the cigar that actually touches your lips and tongue. Some wrapper varieties have very little taste (e.g. Sumatra, Besuki), while others have intense tastes (e.g. CT Shade, CT Broadleaf, Habano, Corojo, Criollo). Whether you taste mostly the wrapper or mostly the filler/binder depends on which has the dominant taste while the cigar is lit. Nicotine can come from the wrapper, by direct contact with a wet mouth, but most of the nicotine from a cigar is contained in the smoke. The smoke is a mixture of smoke from all the cigar's constituents.
I've smoked a blond-wrapped Cuban cigar that knocked me on my butt. I've smoked black, oscuro wrapped cigars that were subtle, sweet and mild.
As a home-roller of cigars, you will have the delightful opportunity to explore all the nuances of different combinations of wrapper, filler, binder. [With your "filler" leaf shipment, don't forget to go through it and separate out the nice, intact leaves to use as binders and wrappers. It multiplies your options.] After a year or so of blending and rolling your own, you will be in a position to simply smile when you read the opinions of the "experts".
Bob