The key part is the second bit - a world where we build loads of air conditioners so that a few people can comfortably cool their mansions in the desert while others boil in their apartments or on the streets is unacceptable.
And re; what you're describing, if you have an AC you (generally) don't need more AC's, that'd be pretty pointless. AC units aren't a thing that makes any sense to hoard away, so the future you're imagining where people in "mansions in the desert" somehow have all the AC and everyone else is just "boiling" away doesn't really seem like a realistic concern. Especially so if people agree that building more AC's will help.
I don't mean look at some specific mansion, I almost even mean the entire countries, particularly Qatar. If you've ever been there, it's mind-boggling how much extravagant waste is displayed everywhere. I mean true extremes of marble and gold foil everywhere, along with the relevant aspect of HUGE air conditioned structures.
I mean so truly excessively huge where vast amounts of empty space are being cooled for nearly nobody within large malls, indoor plazas, mansions, etc.
Also, while I can see a valid point being that maybe they're more corrupt and wasteful than most, I'd just wish to then say I've seen some pretty tremendous waste in western countries, there's just usually more of an attempt to disguise it. And related to your point about hoarding, I'd ask you to consider what the benefit of extra private yachts or the Nth additional mansion or apartment is for a very rich individual are. Why hoard away ships, or trinkets, or homes that won't be occupied? It's a difference of mindset and desires/goals.
But if your goal were, for example, to provide air conditioning to most of Mexico, I don't think reusing existing stuff is going to do it. You're going to need manufacturing.
You'll also need some way of making sure that effort doesn't get redirected, because it will attract people trying to get a cut of it.