As I was working on my pollaxe book I had a revelation: As most of you know, almost all Fechtbücher (with the exception of Codex 11093 and Mair, who treats it more like a halberd than a pollaxe) show pollaxes of the hammer and spike variety, whereas the vast majority of non-Fechtbuch iconography from the 15th century show the hammer and blade configuration (after the 14th century; the earliest pollaxes seem to have been of the blade and spike sort). This has long bothered me, but I have a suggestion of an answer:
Many pollaxes have Languets, or straps of metal that run down the sides (and less commonly, the front and back) of the shaft. I've never seen a lot of value in these because I've always thought of swords hacking into the pollaxe shafts (which wouldn't be that effective), but that's stupid: swords weren't that useful on the 15th-century battlefield (on foot) except among lightly-armored support troops. But what if the axe blades on pollaxes were used to hack opponent's pole weapon shafts (including but not limited to pollaxes), much as Doppelsoldner's among the Landesknechts used Zweihanders to hack the heads off of pikes in the next century?
That would explain the discrepancy: That sort of tactic would be of relatively little value in single combats of the sort covered by the Fechtbücher (it's too easy to simply pull your axe away from such a heavy blow), but highly useful in war. And we've already established that relatively few men probably had extensive Fechtbuch training in the middle ages, so naturally when they did enter into single combats they'd choose the sort of pollaxe with which they were most familiar--the one they'd have used in war. That explains why most non-Fechtbuch iconography, even single combats, shows the axe and hammer sort of pollaxe!
I think the timeline looks like this:
--Pollaxes developed from regular axes in the 14th century as knights sought ways to overcome heavier armor
--The 15th century saw the development of the hammer on pollaxes because experiment showed them superior for overcoming armor; axe blades were retained on pollaxes used in war because they were good at chopping through shafts, but were left off of dueling pollaxes such as those in the Fechtbücher because they had little value
--The 16th century saw a reversion to the axe blade on pollaxes because they were more often either ceremonial or used in unarmored or partially-unarmored combat
Of course there are *serious* exceptions to most of that; these statements represent apparent *trends*, not "facts". For example, the likely reason we see knights engaged in duels with axe and hammer pollaxes in non-Fechtbuch iconography might be that they never studied with a Fechtmeister and that was the kind of axe they were used to from military service.
I must emphasize that there's no evidence one way or other on this subject, and that this theory is purely speculative. It does, however, neatly answer the question, I think.