I just can't fathom any way in which allowing players to be paid will reduce cheating.
Now: "Hey -- we can't pay you legally, and nobody else can either, so here's $20,000 'under-the-table' if you choose us over them."
Then: "Hey -- we can legally pay you exactly the same amount as every other D1 school in the major conferences, so here's $20,000 'under-the-table' if you choose us over them."
I agree 100% that this would not reduce cheating. But why not help out the 80% (my guess) of college athletes who get nothing under the table. Most college athlete are hard working, decent kids. They sacrifice their bodies and sometimes more for our enjoyment. They make millions of dollars for their universities Why not reward them?