Degrees, etc., are better described as positional goods [0], than as more basic luxury goods, but you are right that that largely leaves them as the preserve of the rich (in places where financing is required). I would highly recommend "The Social Limits to Growth" by Fred Hirsch (linked in that page), on the subject.
Fred Hirsch's book "Social Limits to Growth" contains a very interesting exploration of the nature of positional goods, including personal time. One relevant aspect is that as material productivity increases, the relative prices of positional goods increase, because their supply remains limited. It is quite an unsettling read, and I highly recommend it.
This idea is formalised in the concept of "positional goods" [0]. Fred Hirsch coined the name in his book The Social Limits to Growth, which I definitely recommend - it contains a lot of interesting discussion about the place of positional goods in the economy, and how the rising share of consumption of positional goods affects welfare.
Social Limits to Growth, Fred Hirsch, higher education is a positional good. It is about scarcity. The original author recognizes this at
"The real question is whether broadening access ends up reinforcing the educational caste system: if you're not smart or rich enough to go to a "real university," you become one of those poor, second-class students with a certificate Online U."