[raverbashing]

Yes

I believe most of the people, especially the most poverty stricken ones, would stay put

How would they move if they can't support themselves? Food is the priority

Of course, this may lead to a different balance of people in countries, so it may work from that side.

Well as a citizen of two countries (one in the EU) I am quite mobile myself, but sometimes the language is a bigger barrier than the 'official' borders.

On the other hand, some people go out of their way to cross borders illegally exactly because it's illegal.

[parennoob]

Sometimes overpopulation and a lack of education is an important reason for poverty. If a lot of the more well-off people in underdeveloped countries freely travelled to the more developed ones, a percentage of them would make efforts to improve the lot of people in their native countries, since they wouldn't have to jump through a ton of hoops to go back to living in the more developed countries.