A college degree may not be a panacea for class mobility, but lets not forget that class mobility without a degree is pretty much not possible in the slightest.
Per a Pew study Brookings cites (https://www.brookings.edu/blog/social-mobility-memos/2014/02...):
> children born in the lowest income quintile who do not earn a four-year degree are four times as likely to wind up in the bottom (47%) as those who earn a four-year degree (10%).
So while upper middle class people are still the ones with the best chance at getting admitted, paying for, and finishing college degrees, lower class people who persist and do the same really are far more likely to join the middle or upper middle class from doing the same. Though it's far from guaranteed, especially since the relative value of a degree does depend on which degree, and sometimes school prestige as well, which is definitely harder for the lower class to prioritize (costs, scholarship availability, and nearness to family if they need to provide income support or other support to them tend to matter more in my experience).
The observation you mention is accurate, but I just wanted to provide additional context to readers who may not realize the life changing effect a degree can still have for poor people. This is as someone who experienced a comfortable middle class upbringing only because of the combination of a state school in the rural south that gave merit scholarships in the 80s to locals, and my mom's efforts to graduate with a degree that would be worth money.
That said, the idea of pursuing liberal arts in college is still incredibly foreign to me. Being able to support oneself after getting that sort of degree is definitely something I can see as mostly a proxy for upper middle class upbringing, and likely feeds into the rising trends see today where the payoff for the lower class is not hugely significant or comparable to well connected peers, even upon degree completion.