Regarding the chain sword, it was only used twice and under very specific situations. First, the bat Kaiju had Gipsy and was flying up into the stratosphere. They couldn't miss hitting it and the Kaiju while holding Gipsy would be braced so the impact from the sword would be pretty damaging. The other situation was the Kaiju swimming at Gipsy very quickly. Sheer inertia kept that Kaiju going as Gipsy cut through it. The Kaiju literally did the damage to itself by running into the blade. With what it took to get 5000 tons of Kaiju meat going, when it hit the sword it wasn't going to stop on a dime, it just tore itself to shreds.
Now honestly, I would question why they don't start out with two armed Plasma guns when they're at range. Don't let the heavily melee centric monster get close enough to touch you, fry it from a distance.