I rarely see Cutter lines when I play, (except maybe with lower tier players).
The biggest problem with these weapons is the lack of damage and the fact that in order to flinch an enemy you must complete a long combo. This combo also moves you around a lot and makes hitting a single target with every hit difficult.
Much like how I have come to understand the shard bombs (incredible flinch rate) I think I have found out the best use of the cutter line.
Most swords have a 2 or 3 strike combo, this means that anything you hit generally stays in a tight group. A good player using the Cutter can snag an enemy on the edge of the group and combo-push it away. This can be especially useful when separating a mender from its friends, pushing it so far away that it becomes easy prey for your team. The Cutter is also great at quickly cornering enemies, but this ability is a tad more situational than the other as it requires alert teammates who are ready to deal a final blow to an immobilized enemy (various weapon charges are extremely helpful).
The dread venom striker is considered superior while the WHB only really trumps it on poison beast levels.
This is more of a utility/support weapon and can easily be used to single out high priority enemies.
(it is also terribly fun to use)
You raise good points. Here are some counterpoints.
I do agree that DVS is generally better than WHB, but if you're thinking about flinching enemies, you might take another look at WHB. Its charge attack flinches enemies much more than DVS' does.
When dealing with menders and other high-priority targets, I charge-attack them to kill them quickly: Acheron, Obsidian, Umbra, Blitz, Callahan, etc. In my opinion this is even better than "separating them". But maybe I feel this way from playing solo so much.