Let me get one thing out of the way: I've never really loved "Pokemon meets Real Life". So if I seem overly harsh, than that would probably be one of the reasons why.
Also, please, try not to be offended. I don't mean any harm towards you when I criticize what you wrote. I'm sure you are fine as a person and are perfectly capable of writing something really, really good. It may seem that I dwell more on what I don't like as opposed to what I do, that is because I am. I prefer to be criticized than to be praised. That rubs off when I am trying to evaluate something. So, all of that aside, I shall begin.
The main problem with this is that it overall would probably be more work than its worth. If you hope for moving cars, that probably won't happen, not without massive amounts of work it won't. Among those are several other things that would be a bit too difficult to make the world more "real". I mean, city size, people per area, the general landscape of the world. All of it would end up taking excessive amounts of time.
Second, the story itself seems like something that just wouldn't work easily. There seem to be so many questions that the story presents. If your story presents too many questions, it could ruin it. Even if you answer every possible question in the game, it could still turn out bad simply because so much game time would have to be taken just explain why everything is as it is. And if your game has a harder time explaining itself than a murderer who was confirmed as a killer through every possible means, you have a problem.
Just a few of the posed questions: Why are the Pokemon there? (I trust that would be answered.) How come the hero an domesticate a Pokemon while nobody else can? (Classic case of "he's the hero, he can do anything" scenario. Might be able to be classified as "plot armor" but it wouldn't be in the most proper context. I mean, seriously, out of all the people in the world, why does this one kid have the power to this unbelievable feat.) How did the father conclude Pokemon are friendly? Why does he care if they've been mistreated? What insanity lead him to the conclusion of sending his child on some mad quest to prevent everyone in the world/country/state/district/town/2 mile radius from mistreating Pokemon? Why not just present his conclusion to the local district legislator and petition for a law to be passed, that way the entire law force can deal with his fear that Pokemon are mistreated for some reason.
Now let's say the story was edited or the questions were answered in such a way that the plot could continue as you plan. How would the game go about? If Pokemon are now in the wild, would they appear wherever they wanted? Would there be tall grass? Why would there be tall grass? In the real world (In the USA, at least) there are very few areas that could be used as routes in this day and age. Most areas that could, are dominated by roads. Would he go by foot? Why would he go by foot if there are cars, buses, planes, etcetera that can be used to go where you want?
Then what would happen? Would you go around cities, preaching that Pokemon shouldn't be harmed I'm sorry to say, but that's not very exciting gameplay. Would there be battles? Well, yours is the only domesticated Pokemon in the world, so no trainer battles. Speaking of which, why aren't you a celebrity by now? Wouldn't every swarm around you the second you show your face just because you have a Pokemon? Why are the police/scientists/the government not trying to use you to train their people to be able to train Pokemon?
Back to the subject of battles, would you battle wild Pokemon. We already covered the issue of where would the wild Pokemon even be. Why would your Pokemon even listen to you, did the hero train that thing for years to respond to certain vocal commands with certain actions like a dog? Why would the hero want the Pokemon to use attacks? Wouldn't using a Pokemon be abuse? For both the one being commanded and the one being hit by the one being commanded?
So, by that logic, there could be no Pokemon battles. And, without Pokemon battles, the game would lose all connection with Pokemon in all ways. No matter how far away from the traditional formula a Pokemon game is, and no matter how much I hate people making nintendo Pokemon clones and call the new games (hacks) there still has to be Pokemon battles.
Now, maybe, if the story was drastically changed, it could logically work. But, I refer you to my original point: it would probably be more work than it is worth.