1) While axes are technically bladed weapons, which causes people to think they belong in the Blade skill, more accurately they are hafted weapons, which means that the way you hold, attack and block with them is the same as with similarly sized blunt weapons (maces, warhammers etc.) Think about the way you would hold an axe or mace, the crushing motion etc. Now think of the way you would hold a longsword, and you will notice they are completely different. You can't stab with an axe, and it wouldn't make any sense that you would get better at using a longsword by using an axe.
2) Roleplaying reasons. Some people may pick major skills based on roleplaying, and for a Barbarian type character, they are more suited to a Battle Axe or Warhammer than say, a Claymore. As such, someone playing a Barbarian class, who might want to switch between a mace and a war axe would only have to train the one skill.
3) Balancing issues. If the skills were still split up into Blade and Blunt, but axes were part of the Blade skill, there would be far more blades than blunts available. In fact it would be a little like this:
Blade: Dagger, Shortsword, Longsword, Claymore, War Axe, Battle Axe
Blunt: Mace, Warhammer
This coupled with the fact that there are already more unique Blades than Blunts, and there would be no reason to pick Blunt at all, as it is clearly the far inferior skill.