My theory involved what would happen if Pokemon and humans lived in the same world from the beginning and was basically that natural selection would cause humans to die because everything else survived better, but your post made me realize that even though the background I imagined was the most realistic, (unless genetic programming of the future proves me wrong) it was the only one where humans were likely go extincted. I recall hearing in one or more games that it's rumored that Pokemon come from space. If that happened, and if they came around after humans have advance far enough to protect themselves, then the Pokemon world we think of happening makes sense. (Also, my theory on humans dieing quickly now only applies only to every other animal on earth. That means death to squirrels, but it's worth it. :P) As for genetic advances, due to Pokemon being around for thousands of years before the games take place, I think we can rule that out as a possible background for the world in the games, (except for Mewtwo and Genecect) but if Pokemon being made through genetic programming happened in this world, a similar world to the one in the games would probably result. The only differences I can think of are there would be no legends and no extinction of squirrels.
There is also the possibility that some Pokémon were just far too strong, and had too much will, to be controlled. Whether they came from space, or were the result of genetic manipulation, some military, government, and/or terrorist organization likely would try to come in and take over.
The trouble: Kyogre breaks free of the Blue Orb's control, causing massive flooding and tsunamis, just like in the movie 2012, and that alone would reset civilization, but then Groudon also breaks free, causing massive tectonic activity, destroying, and burying most, if not all signs of past human civilizations in lava earth, also just like 2012.
You might even have a Moltres, Articuno, and Zapdos breaking free from imprisonment, and attacking each other and their tormentors, adding to the chaos.
There is even the possibility that almost everyone died, that this is where the legend of Pokémon tears came into play, reviving most (but not all) species, and maybe whoever wasn't buried, incinerated, or at the bottom of the ocean. What few technological devices that survived would likely eventually stop working, and become nothing more than legend, or destroyed as the new reset civilizations fought over resources. I always thought that Pokélantis might have been one of those civilizations that managed to salvage ancient advanced technology.
If not for the fact that it has been explicitly stated that Pokémon have been around for millions of years, the series could easily be thousands or hundreds of thousands of years in our future, and all that we know has been destroyed. The Elgyem and or Clefable (or even Arceus) could have transplanted them all from a dying world (it must take billions of years to be able to use elements like that anyways). Apparently, not everyone got along on Earth.
Absol could be useful in helping to predict disasters while the flying types and pokemon with teleport can help to move the people to safety before the disaster occurs. In case some people are stuck under I can see fighting and physic types helping to clear the debris while flying types carrying people to safety.
As much as I despise it but pokemon could be really useful in war. I can imagine charizard, salamence & other flying types covered in armour shooting strong attacks like flamethrower and hyper beam. While stuff like blastoise, gyarados could be useful in the navy.
I think that this has all but been confirmed in flashbacks for the war in Kalos 3000 years ago, and in Lucario and the Tree of Life.