The history of guns in japan.

[John Adams]

The hell is this? Wouldn't a bayonet make more sense than an axe?

It is a bayonet. Note how the axe is forged, and how the end juts out past the end of the gun. It is a bayonet, and can be used exactly as you would use a bayonet (in otherwords in a straight stabbing motion), but it is also an axe. The way the axe is attached means that the gun is now a polearm when in close quarters combat... Capable of using the axe to it's full strength. The curve of the buttstock lends itself to a downwards striking motion with the axeblade as well, allowing the user to put greater strength into the blow.
In otherwords, it is a very functional design. The only problem is the extra weight on the end making the gun itself heavier, and harder to aim by a tired soldier. Having not handled this piece, I would imagine the buttstock to be crafted heavier as well to help balence the piece, but that is only a guess, and it may very well be top heavy.
A bayonet would make different sense than an axe. A bayonet is limited (functionally) to a forwards stabbing motion. Although it is possible to use the sharp edges of a bayonet to slash, the damage is minimum. Unlike say a short sword which is a cut and stab weapon. This polearm has no such limitations, and can be used as well as on the stab as the cut.
~John

[Lord Oda Nobunaga]

Those weapons are heavy so I couldn't imagine swinging that around after holding that in a field while standing for a while.

[John Adams]

Those weapons are heavy so I couldn't imagine swinging that around after holding that in a field while standing for a while.

... They aren't that heavy.
And besides, that's the entire point of training. So you can do that with little difficulty.

[Lord Oda Nobunaga]

I don't know, I was holding a flintlock and it was pretty heavy on me after standing and walking with that thing on my arm for a whole hour.