Unless you want to make a fort at night, I really would not bring an axe along. Finding firewood for a campfire is usually not a problem.

But a too heavy bike is.

I did it bike camping a lot and my advice is, only bring what you absolutely need. Without extra burden, everything is much more enjoyable and you will have more energy to reach the nice spots.

I do a lot of slow bike camping in Japan where the campsite will often provide firewood, but it's too large for the small solo stove I have. I've tried a saw, but what I really want is thinner wood split from the larger pieces, not lateral cuts. The axes being talked about are only about 470g, which doesn't bother me too much shoved in a pannier.

Ok, this is a very different scenario then, where it makes sense for you ..

X11 or X7 would probably be a bit lighter and more durable. I know its ‘plastic’ but I’ve beat the shit out of mine for 15 years and it hasn’t loosened up at all. Wood handles get finicky in the elements. The Fiskar plastic handles are hollow, too, you might be able to pack a flint kit up in there for energency use.

Something like an Eastwing is goong to be a better chopper, but these will split better. Both are useful.

To bike camp bring a small foldable saw, so instead of spending 1+ hour splitting wood after a long riding day you can spend that time enjoying camping

I have a carpenter axe which is very compact and somewhat lightweight, but gave it up because I never had to use it

Link?