Oh, so if technology exists that can contain and neutralize the hazardous material that make up the Kaiju, why should we worry about using ranged weapons?
The technology exists to clean up oil spills and toxic waste.
Do you think it would be no biggie if we splattered the entirety of downtown Los Angeles with highly toxic waste?
We are shown shots of Kaiju corpses decomposing so quickly that their flesh liquefies and their organs spill out. I'm willing to bet the reason Hannibal can even do this is by getting there before they start to decompose and spread their toxicity to the surrounding area. He *did* make a big deal about getting to the corpses and harvesting them quickly.
If they waited for the thing to fall apart and ooze all over the place (or made a habit of blasting them apart) I'm sure the clean up would be significantly more difficult.
It's easier to clean up a leaky milk jug than one that has exploded, ya know?
As for the viability of long-ranged weapons, when would you shoot at them?
The Kaiju remain below the waterline until they either A.) Find a target or B.) Are forced to surface.
So again, you'd only get to take shots at them after they've already waded into a city, at which point you really can't afford to go blasting wildly.
I'm not sure why a Jaeger would stand off from a Kaiju and take pot shots ever, considering that just invites the opportunity for them to accidentally plasma-blast civilian targets and waste their somewhat limited ammunition. The Jaegers are *designed* to get up close and grapple with the Kaiju, so why not get in their face and THEN blast them? It worked for the Landsknecht, after all.
The Jaegers *did* use ranged weapons, but *only* when they had either grappled with or stunned the Kaiju, ensuring a 100% chance to actually strike their target. Considering that Jaegers routinely engage these monsters within eyeshot of civilian targets, this seems like a good policy.
Again, not perfect, but sensible enough for me at least. Obviously the true answer is that it wouldn't look as cool, but I appreciate that GDT put at least a little thought into making it plausible.
The Jaegers serve the same purpose as the defensive line in football. Kaiju are making a beeline for a population center and Jaegers are uniquely suited to get in their way, make them surface, and physically prevent them from advancing.
I can't think of any other weapon system that could manage such a feat without a nuclear detonation, and even that isn't guaranteed after we saw Slattern shrug one off.
ADDENDUM:
I watched it again today, and actually *NOBODY* touches any Kaiju or Kaiju body parts, organs, or fluid with their bare hands in the entire film with the exception of Hannibal Chau as he cuts his way out during the post credits scene.