Second, the calculation of who benefits from tuition reduction assumes that that the population of college-goers stays fixed. But the goal of free college plans is to increase college attendance and completion, especially for poor students.
This is an important point. The first paragraph of this section ("In a narrow sense, yes...") immediately raised concerns in my mind about the argument. I suspect that the reason people from poor families attend college at lower rates than their wealthy counterparts is because they do not have the financial means to do so. While free college would be regressive in a sense, due to the fact that there would b money left on the table from wealthy families who are able and willing to pay for their children to attend college, it would be progressive in the sense that poor families whose children otherwise would not be attending college now will be.