Yep, sword of war is better, that's why it's also more expensive. The reason why you don't see many people running around with a war cleaver is the same reason why you don't see many people running around with e.g. battle fork. Both weapons have more expensive better options.
As for the rest of your listed weapons, i really don't see why you consider them better than war cleaver. War cleaver mostly does more damage, is longer or cheaper. I still think it's pretty well balanced.
Now, if we are on the can my favourite weapon please be buffed train, can the long spiked club please be buffed? Less speed, more damage, please!
But back on topic: I no longer consider the regular great sword, which has 1 more speed, but 1 less cut and 3 less length, superior to the german great sword, because 92 speed is enough.
No, it's about general balance. The cleaver gets a huge penalty, unbalanced tag, with nothing to show for it. Pretty much every other "unbalanced" weapon gets either bonus vs shields, crushthrough, blunt damage, pierce damage, etc. Which seems like terrible balance for this particular weapon. I'm not even sure why the unbalanced tag was added in the first place, in native it was balanced. Here it recieved a HUGE penalty which makes it sub-par to every other option.
Why would I consider them better?
NoDachi - Longer, not unbalanced
DaoDao - cheaper, same stats for the most part, non unbalanced
Miadao - same as above, not unbalanced
Great Bardiche - more damage, bonus vs shields
Sword of War - Thrust, non unbalanced, faster, longer