It would be totally unfair for an engineer to miss 8 years of salary, amass a huge student loan, and still be paid equal to a janitor.
The reason programmers command a higher salary than janitors in the US is due to labor demand; programmers can leverage that to their advantage. If I understand the article correctly, there's no need to do so in Japan because what programmers would leverage demand for (better social status/quality of life) is simply given to them.
It's also worth saying that salary aside, programmer is a better job than janitor for most people because it's more stimulating and rewarding. So it's not like you'll have a bunch of potential programmers deciding they can make almost as much money as a janitor and thus forego education, etc. In fact, isolated, it's likely to keep out people who are only into programming for the money, although in Japan the increased social status/quality of life replaces the salary incentive so it probably doesn't work there.
I also disagree with your implication that this system is economically infeasible. It's been working for decades (millennia?), and has built Japan into a world economic power. I'm not saying it's been without negatives, but I would argue that no labor system is.
I guess the unstated implication of your scenario is that businesses would start paying programmers more to work for them. However, at least in Japan, this has not happened. Programmer salaries stay close to other employees.
I don't think I can snap my fingers and change things everywhere, but I think there's ample evidence that similar salaries for disparate educational requirements works on a societal level. Thus is not really a, "what if," scenario.
In exchange, you get a lifetime security net that gives you the same guaranteed life as your coworkers. Serve the hive, and you need never fear. If you ever left it, you would never again have access to a security net from anybody, and with so much of your life depending on your hive membership, you're unlikely ever to leave or to be thrown out.
In such a system, where you don't know how you could survive outside the hive, maintaining the hive matters more to the bees than increasing profits. Yes, maybe the hive could get some economic benefit from hiring more women due to their being undervalued in the market, but maybe the unintended consequences of changing something like that might destabilize the hive. It's just not worth the risk if your whole life is going to depend on this one hive.
And maybe your hive could benefit by hiring skilled people in mid-career. But none of the hives do that. They've never done it and don't even know how. What would you pay somebody joining the hive in mid-career? How could you even judge the value of someone financially? We've never done that; nobody does that; there's no "market". What impact might it have on existing bees, who have been together since age 22, to have a foreign bee join them in mid-life? It's just not worth the risk to the long-term stability of the safety net on which all life depends. Don't change anything. Do what has always worked, defend the hive, and it will defend you.
I'm not sure if this is your idea of something "working on a societal level" but it's not mine. Ironically, I think this "stability over adaptation" approach puts Japan at greater risk of instability over the long run.