One key point is that being able to work to subsidize the basic income makes the income much more powerful than "phantom" dollars that disappear as soon as you start to work.
The trick is that the funding level of basic income doesn't have to "fully cover" a family of four. The family of four will be able to supplement the income, rather than today being locked into receiving it. Also, it doesn't mean that programs like SSDI go away, you still can provide national disability insurance.