Oh boy indeed. I understand you like this movie, but you're really reaching with these explanations 
We don't need a scene showing kaiju blood being toxic because they told us in the exposition-heavy prologue that it is. Showing is better than telling, but if you've already told then showing is redundant. Also, Idris Elba says that Perlman's team neutralizes the toxicity before going in for the remains. Not entirely justified, but not without logic.
Hey, you brought it up as a justification of why the Jaegars weren't using their most effective weapons. If that's the case, the film needs to make it the reason and show it. What the film does show is a callous disregard for collateral damage, so I'm not really sure how that's supposed to fly.
The beast is there to destroy the buildings anyway, so damaging them in a fight to kill it isn't ridiculous at all. What, is the kaiju just supposed to rampage around the city and go home?
Charlie Day says pretty early on that the kaiju's plan is to attack the populated areas and take out the "vermin." That line was in the trailers, for god's sake. And we do see them take on a kaiju before it gets to a city in the first scene of the movie. Idris Elba specifically says that their primary priority is to protect the city. And he says it AGAIN before the Hong Kong fight.
You misunderstand, and I may be to blame here. The object is to protect the cities and save lives, right?
Option 1 - allow kaiju into city, not be allowed to use best weapons for fear of toxic blood, fight them ineffectually by punching them, practically destroy entire city in process, many thousands die, many more thousands left homeless and leave - city now a ruin
Option 2 - allow kaiju into city, use best weapons to kill it quickly, toxic blood causes some damage, many thousands leave whilst it's being cleaned up (neutralised even!) then return to city which is mostly still intact, repeat as necessary
Option 3 - kill kaiju before it gets near city with best weapons
Which of these options is the worst for protecting the city? The first. And this appears to be the most common method (all the destroyed Jaegars we see in montage are in cities plus Tokyo and Sydney). Even outside Hong Kong in the sea where they can go all out without fear of collateral damage, the best weapons aren't used and two Jaegars are destroyed because of it (and a kaiju enters the city and destroys much of it).
You can't really argue that Jaegars aren't fighting at their most efficient due to fear of collateral damage (unspecified toxic damage) when the Jaegars are essentially using collateral damage to kill the kaiju.
Killing the kaiju should have been paramount, and that could have been a theme of the story, mankind was essentially turning into beasts themselves to survive. They were cutting off arms to save the body, they were making hard choices about who to save (and none of that stupid 10 vs million choice), and they were turning to increasingly more terrible weapons to get the job done. The one interesting element, that the early pilots had been killing themselves by using the machines, is brushed aside with little exploration.
At this point, I think a comparison is in order. World War Z, the book. The human race is shown as making mistakes at the beginning, and suffers because of it, but they aren't incompetent. They've thought of how to deal with the threat and throughout the world have adapted and developed new tactics to cope, cities have been abandoned as indefensible and new defence lines have been set up, for instance, the Americans have abandoned virtually all of the coastline and retreated to the mountains.
Where is that here? Where is the common sense?
This is a war that has gone on for years (I think about a decade?) and the film instead chooses to portray mankind as idiots who opt for a plan to build a wall as their last resort. Something that would have made sense in the first 2-3 years perhaps when we were still learning and didn't quite know what we were dealing with. It makes it worst that the film presents it as an inevitable failure which the military guys don't even fight against. You know what humans came up with the last time they wanted to end a global war? Nuclear weapons.
So the question is, why does mankind have to be retarded? How does that make for a good story? How does that make the world feel real? Making characters stupid so that plot happens is the worst way to write. You seem to agree that this happens in Prometheus, but remain blind to it here.
And why weren't there all those weapons? Because this is a movie about giant robots, and the movie where humans efficiently and effectively deal with the kaiju perfectly and without any problems would be boring.
That's the difference between good writing and lazy writing isn't it? You make your story dramatic by giving your villain great powers, not by making your heroes stupid with convenient moments of sense.
What would I have done differently?
I'd have made the story about the search for a way to end the war. Parts of the world have roaming kaijus and others are uninhabitable due to the use of nuclear weapons used early in the war. The US has a defensive line at the Appalachians, behind which everyone has moved. Jaegars work in pairs or squads with support from other branches of the military, kind of like the mechs in Patlabor and Appleseed. They're loaded down with offensive weaponry. But the problem isn't really the kaiju, even though they're bigger and harder to take down, it's that it's neverending. They just keep coming. Mankind is getting tired, we're running low on materials due to attrition, and we're killing the planet to win.
And I'd have a scene where a Jaegar runs out of ammo and is forced to use the fists, something that no-one has ever done successfully before. This would be the goddamn climax, and like Neo in the Matrix, it would be this "what are you doing, you crazy mofo fuck me what a punch and jesus he uppercut him right in the jaw, and now look he's using a goddamn ship as a bat!" crowning moment of awesome. Instead of the... STOP USELESSLY BLUDGEONING THE CREATURE OVER AND OVER frustration we have now.
Ahem... excuse me.
