This might well be a good thing to do, but it should be noted that income qualifications come with their own entire bag of tricky problems and potential perverse incentives.

What income level do you set it at? Is it a cliff or phased out? If the latter, what does the curve look like? How does it change with inflation? Are these questions set up front or negotiated by politicians at some frequency? How is wage vs. capital-based income handled? These are the kinds of tricky questions that come up (and are usually not answered very well) with any program that attempts to inject some income-based fairness into some government system.

So I think the answer to your "why not?" is that it will be hard to get it right and is likely to become a political football that may end up making things worse in some way. But the argument for doing it may still be stronger (it seems so to me, without knowing much about it), I'm just saying that there is also a fairly strong counterargument to this sort of thing.