https://badaxetoolworks.com/collections/tools-and-accessories/products/bad-axe-saw-set . . . appears to be usefully focused on backsaw-size tooth-pitches ie 10-20 ppi.
Regularity & speed. Hammer-sets mimic the dynamics of the technique used in 18th/19th-century saw-manufacture (hammer-setting upon special anvils). Here's Charles Holtzapffel (writing between 1827-43; pub: 1846) on the techniques used around/before H1 C19th: . . . . delightfully, Holtzapffel goes on to describe (for circular saws) the first embodiment known to me of a hammer saw-set; viz:
Peddar asks an interesting question, and having set tens of thousands of saws I think it's clear what the best method for my own purposes is. Set enough saws and you will know too. Saws were traditionally set with a narrow faced hammer over a simple bevel filed into the edge of a vice or block. It certainly was a fast method. You have have rapid or consistency in setting saws, you can't have both. And no method is rapid on fine teeth because you have to take the time to align each tooth with the anvil, they're hard to see and there's a lot of them.
I'm not familiar with Badaxe's revamped design but I would add an adjustable dog/pawl so you can rapidly align the plate with the next tooth to be worked. This would speed up the process of re-locating the plate every time which is a major rate limitation.
Linkage to a chatty YouTube channel's saw-setting video; where the original Seymour-Smith hammer-set is described (at around 7 mins 30 sec); then the Bad Axe hammer-set (around 9 mins).