They had UNIQUE skills. A good baseball player is a dime a dozen and there are plenty of American players that likely can step up and do the same. As earlier commenter noted, the Venezuelan is lots cheaper. Poor excuse.
At the entry level they used to be more expensive, since they weren't subjected to the draft process and could sign with the highest bidder. The two most recent CBAs set limits on how much teams could spend on overseas players, but they can divide up their allocations as they see fit.
MLB has almost all of the world's best players and roster spots are pretty ruthlessly merit-based. Allowing the best in a given field into the country has never been a problem.
I am not sure that those individuals had skills that were any more unique than a great a baseball player’s, but the matter of the atom bomb was of graver consequence than the outcome of a baseball game. Regardless, if we do not admit the best qualified players, we will not have the best baseball teams in the world. We will become mediocre.
Where I live, the Department of Labor used to (and may still) issue temporary work permits for Jamaican apple pickers. The program goes back to World War II. The Jamaicans made about $10/HR in 1987, and a few weeks work would go along way back home. The workers were clean, workmanlike and rarely caused trouble. (None that I am aware of.) The farmers preferred the Jamaicans because they were better workmen, they did not damage the trees or tools, and were very productive and reliable. People on workfare of college students could not match them. (I have heard similar stories from a guy who worked in a vineyard in California one summer with Mexicans.)
Bringing people in for the sake of diversity really just means recruiting clients for the welfare state, and reliable Democratic voters. Seasonal agricultural workers, don’t leave children, don’t burden the public. A little diversity as a by-product is fine, but it should not be the purpose.