The idea that the people employed in the bureaucracy managing the current mess of programs losing their job is a silly concern. Why should we keep paying people for unnecessary bullshit jobs? Why should we employ people to check and ensure that other people aren't secretly working? Let those people do something more productive.
I would like Basic Income to be a bit more than $10,000 per year, though. Ideally, especially when the number of jobs available falls due to increased automation, I'd like the Basic Income to provide a comfortable income. People can and will still work to increase their income further, but when robots do more and more of the work for us, there's no reason to punish people for being unable to compete with robots.