I'd think there would still be migration, but a larger portion would be documented migrants, mostly temporary, and mostly connected to cross border businesses. Salesmen, managers, some specialists. Plus there would still be political refugees. Stability and prosperity does not prevent a exit of persons at risk for political reasons. To put it another way the migrants would have a far higher portion of educated among them. I'd also think there would be a larger than historical reverse flow of US citizens moving to Latin America for the same reasons. Often as employees of existing businesses performing managerial & technical services that are not readily available from the local labor market.
Within the US there is a large and constant flow of labor at all skill levels from region to region. I'd think a significantly more prosperous Latin America would change the character of migration, but not reduce it.
Well most of the immigration in the USA is legal, there are 52 million of legal immigrant in the USA V/S the estimated 11 millions of Illegal Immigrant, (source 1: https://www.migrationpolicy.org/art...tics-immigrants-and-immigration-united-states / Source 2:http://www.pewresearch.org/fact-tank/2017/04/27/5-facts-about-illegal-immigration-in-the-u-s/) and is more or less the same class of people you mention, in fact one of the biggest problem for the mexican economy is tha there are more PHD graduates migrant to the USA that there are Simple laborers (source https://www.telesurtv.net/english/n...rogram-to-Stop-Brain-Drain-20141223-0033.html)