Most Hispanics in the US are mestizo or mulatto. You cannot make a brown man a white man (nor should you). Cultural upbringing and genetics can never be ignored.
Even with Mestizos many have a large European genetic source.
If immigration was slowed down, the Latino community would actually have the chance to assimilate. Not all of them would assimilate into the “white” category like Eastern Europeans, Italians, and the Irish did, but a good amount would to render the category useless.