While Atkison-Stiglitz does promote labor income taxation, it leaves plenty of space for creativity within the regime. In particular, utility optimization should (all else being equal)
- favor people who value the marginal dollar more than their income would suggest
- favor people with low incomes due to immutable characteristics over people with low income due to their own choices
Some examples of (1):
- Suppose House A consists of an adult with an income of \$60k and House B consists of an adult and 3 kids with an income of \$60k. All else being equal, House B gains more from each additional dollar than House A.
- Suppose House A and B both make \$60k but that someone in House B needs to buy cancer-treating drugs. Household B will (all else equal) value each additional dollar more than house B.
These examples aren't super controversial and our existing tax-system recognizes them by provide deductions for dependents and medical expenses. Our welfare system similarly takes these factors into account.
(2) is more controversial.
For instance, since tall people earn more than short people, (2) suggests they should pay more in taxes.
An important point here is that we don't care whether being tall causes higher incomes. The fact that we should tax tall people more is provable merely from the fact that height (1) correlates with higher incomes and (2) is essentially unchangeable.
Taxing height would be controversial enough, but there are lots of immutable characteristics that predict income that are very political charged such as race, sex, age - to name just the salient ones.
Needless to say, regardless of how optimal such factors make taxes in an ideal world. We won't be using them any time soon in this one.