I have read a few questions regarding pronunciation which is complicated by accents across the US. I assume this is also true for other languages. In most dictionary references, a pronunciation key is provided. If the words are taught with this information included, wouldn't we all sound the same? For example, http://www.merriam-webster.com/dictionary/cars
I think you're minimizing how complicated this would be.
First of all, you're confusing pronunciation and accent. It's an oversimplification to say that people with different accents pronounce things differently. That's partially true, but it would be more accurate to say that people with different accents say the same pronunciation differently!
A pronunciation key tells you which individual sounds make up a word. Different people say those sounds differently. Here is a reasonable description of what I'm talking about.
In other words, two different people can read the same pronunciation key and say different things, and both would be correct. So a pronunciation key doesn't really do much if your goal is to get rid of accents.
So sure, we can see that the pronunciation of "car" is /kär/. Now, what does that sound like? Somebody from Boston has a different answer from somebody from California. Both are correct.
I suppose you could force everybody to learn one phonetic alphabet (whose?) and force them to only use that, but how would you go about it? How are you paying for the massive amounts of training required? How are you going to handle the backlash from people who don't want to change the way they speak? How are you going to enforce this over time so the accents of different areas don't drift away from each other again?