I prefer a gamist perspective over a realistic perception in D&D too but the system you have made is heavily reliant on historical aspects so I feel it is necessary to bring them up.
I am simpy afraid that the amount of groups may become a little overwhelming, but if you think that is better solution than it is fine. That is definitely a rather strange group to add on though keep in mind, and I do not see any reason why it can’t be a pole-arm, but if you are intent I suppose it is fine.
I would be fine putting it in there if the group was called something like “chopping” weapons but i personally find the category of “axe” misleading. Now that I know what you mean by axe, I am fine with it being there but I am stating that people would not intuitively know that axe=chopping weapons.
If you wanted to keep the tradition you could always just put the motion in parantheses. Called them axes (chopping), heavy blades (slashing) and light blades (stabbing) or something. Like that
If you do not like the word blade you can use the suggestion I stated in the previous paragraph. I can imagine why you would find putting sickles in with great swords strange though, but it is just that if your mentality is really heavy=slashing and light=stabbing than sickles would be heavy.
I still do not understand your issue with making staffs pole-arms. Many of the same feats that would apply to pole-arms make a lot of sense for staffs too. But putting them In with crushing is fine.
Fair enough, there are several feats that work with spears and tridents anyway do they do not need any extras. Your case about the nets are fair too. I do not understand why blowguns are exempted from the list though.