To my mind, Universal Basic Income (UBI) is the most radical attempt to address the complexity that is introduced by trying to only give benefits to the "deserving": there's often a view that social benefits (food stamps, income support, child benefits, health care, etc, etc) should only be given to those who "need" it. So then you need to:

- decide who actually "needs" the benefit

- figure out how to recognise these people ("means-tested" benefits!)

- catch the people defrauding the system

Instead, you could just say, e.g. for the case of child benefit, that every child receives $400/month and get rid of:

- the complexity in deciding who gets $400/month

- the enforcement of fraud

The "underserving" middle- and upper-income will receive this money too, but it doesn't matter - it's effectively coming out of the higher taxes they are paying already.

UBI is just a generalization of this idea to all benefits.

Introducing two kinds of dollars smacks, to me, of the same mindset that introduced means-testing/etc in the first place: "we don't want fraud", "we want this to only go to deserving purposes". Lots of complexity, hard to manage, and for no convincing benefit.