There's other things they should do first though.
Not everyone is fit to go get a bachelor degrees. Some people don't have the aptitude for it. Some are just not interested. Some don't have the patience. Some made mistakes and are stuck with kids and can't commit that far. Some just don't feel like it.
The US is messed up in that its a country where if people don't recognize the college you went to, they make you feel like you're a nobody. That leaves a significant portion of the population feeling like they have no meaningful option. A lot of people seriously beleive you're better off with an barely passing grade in liberal art at Harvard and working at McDonald's with insane debts than being a successful carpenter who owns his/her own business.
Thats ridiculous. Yes, virtually all other first world countries have free upper education. But they also have a LOT more respected (I stress that word) options for people who don't want to go that route. Apprenticeship, useful lower level degrees, adult continual education... Sure, you can do an Associate degree in the US, but its barely worth the paper its printed on. And even if you are successful, no one respects you for it.
So IMO, the first step is to have more _respected_ options. Thats a lot harder though, because it requires a culture shift. Stop making fun of the guy who choose to become a plumber or repair rooftops because he didn't go to MIT. Encourage people with non-academic, yet useful skills. Yeah, they're not going to buy a 5 million dollar penthouse. But they're going to be able to feed their family and save for retirement with money to spare, AND their job is hard to outsource.
Once that happens, then you can start looking at how to elevate the average.