Universal programs would get rid of unfair welfare surveillance.

Buttigieg is relying on a conservative talking point here, that universal programs are inherently unfair, either to people who don't use the program or people who can afford to not need it. Intentionally or not, he's making an argument against all public education. And if his means tested plan for free-college-for-some-people became a reality, it would be incredibly vulnerable very quickly. Since only a narrow segment of the population would benefit from it, building popular support to defend it would be a difficult task. In The Week, Ryan Cooper argues that universal programs are politically stronger and more resilient to cuts because they benefit more people than just the very poor. For that same reason, universal programs deliver better results. He writes:

Middle- and upper-middle-class beneficiaries can also complain when the program isn't working correctly, and they are much more likely to get an attentive hearing. [Universal programs] are also less complicated, because they don't require as much of a surveillance wing to adjudicate eligibility. Make a program part of the fundamental infrastructure of life for everyone, and it will generally be high-quality. As the transit nerds say, you can tell a public transit system is really good if it is used by rich and poor alike.