It's in each person's best interests to vote for more wealth redistribution if they're below the average, and there will always be more people below the average than above.
Further, it's in each politician's interest to both promise and deliver such a thing, as it helps them win first and following elections.
Those leeches are the least of our worries.
How about long turn demographics? There are racial and religious minorities, that have 12+ children in an average family. A basic income may help them grow even faster, leading to inevitable huge changes in the society.
Also, I'm under the assumption that "leeches" basically just means poor people. I supposed if we had to be more specific, in America that means Hispanics. They are not exactly religious zealots, but are definitely making relatively larger families. That's just going to be the demographic reality in America.