Two-handed sword could for example have cleave, hit X enemies in front of you with normal attack, two-handed hammer could have a "stunning blow" etc. Adding it as a skill to the weapon abilities despite it being weapon class feature makes it easier to read.
The problem I have if a weapon were to have Cleave, that is a feat that classes strive for, I wouldn't just give it to a weapon.
I do understand "rush" with the spear weapon I originally posted, since now I know its a spear, that make sense.
There are many types of weapons and if you want to give an individual skill to each of them it will lead to some inconsistencies.
For example tell me an action that can be done with a longsword but not with a shortsword or a scimitar.
We have to accept that RPG rules are always always arbitrary and abstract to some degree and they are not a perfect simulation of reality, not even the fictional reality of the game.
Personally I am happy if weapon choice becomes more meaningfull, because else it makes no difference if you use an axe or a sword.
I did not find the cleave feat in 5E (but great weapon master lets you attack again if you crit) but it was a feat in 3E. The spear ability looks similar to the charger feat.
I agree that a weapon ability (which you get automatically by equipping a weapon) should not make a feat obsolete. But feats in 5E are usually a set af effects.
I think it would be OK if one weapon gives an ability, even when there is a feat as long as the feat gives this ability to several/all weapons or it has other effects as well.
Prof. Dr. Dr. Mad S. Tist 
