Monetization is equivalent to a global tax on net dollar denominated assets; doing it to a major ongoing program is a good way to trash your currency.
It's not necessarily bad to use direct benefit payments as a monetary policy tool when there are monetary policy reasons (e.g., your proposed QE alternative), but unless you're willing to see BI go away completely when the traditional concerns governing monetary policy call for tight money, then you shouldn't call for it to be monetized unless your goal is to destroy the dollar rather than provide a stable public benefit program.
Since I am suggesting that BI be a major lever of monetary policy, it should follow that I am willing for it be tightened as necessary. Do you think it would go to zero? That would be more extreme than any of today's austerity programmes.
It's not necessarily bad to use direct benefit payments as a monetary policy tool when there are monetary policy reasons (e.g., your proposed QE alternative), but unless you're willing to see BI go away completely when the traditional concerns governing monetary policy call for tight money, then you shouldn't call for it to be monetized unless your goal is to destroy the dollar rather than provide a stable public benefit program.