Wow. It took so long (months!) for my account to be enabled, I'd completely given up on this forum. Anyway..
I can't think of any major benefit for tapering the jaws. With fan gluing you leave so much of the book block exposed during the gluing that it will lay over quite far before you have any chance of the paper hitting the edge of the jaws. My of the designs I've come across are pretty simple jigs with an emphasis on keeping the pages together when fanning and gluing.
Since posting the above, I've investigated further, creating a few designs which permit deeper glue lines. The working assumption being the legacy jaw taper functions as a concession for a more pronounced fan spread (and correspondingly deeper glue line) particularly for smaller work. What let me down this path was the NISO Library Binding Standard specification
. In particular section "7.3.3 Fanning and Gluing" calls out a glue line depth between 0.8~3mm. However in my experimentation this seems wildly excessive from a structural perspective.
Standard copier/printer paper (eg: US 20LB bond) is about 0.1mm thick. And I've found a glue line starting at 8x depth for this media yields a considerably stiff spine. Moreover it results in a significant "break-in" phase of the text block where the exaggerated glue line depth causes individual pages to undergo substantial internal tensile failure delamination at the glue joint. This occurs parallel to the page for the depth of the glue line as each text block page experiences its initial full flex cycle. I've subsequently found this has been documented by Pete Jermann
. All that aside, it isn't really a structural concern yet creates a usability issue. To "break-in" the text block requires full flex of each page-to-page joint, otherwise the in-hand page turning feel of the text block is choppy and inconsistent.
However I'm inclined to dismiss this aspect of the NISO specification, along with pursuing any practical advantage of a substantially deep glue line. Empirically it appears most double adhesive fan gluing operations flex the text block a maximum of 90*. And the general calculation of glue line depth as a function of text block bending/wrap is: glue_line = 6.28 * page_thickness * bend_degrees / 360). So for a 90* bend the glue line will be 1.57x of the page thickness or for 0.1mm paper a depth of 0.157mm -- a far cry from the above suggested minimum depth of 0.8mm. Yet in practice a 90* text block deflection during fan gluing produces sufficient structural integrity of the text block, while resulting in the characteristic "rubber band" spine effect.