Let me counter your argument as an American living in Japan (though not working).
> Not because their job is inherently more noble than the lowly paid ones
In Japan engineers are treated like janitors because that's how Japanese businesses view other non-sales non-management positions within the company. The bosses decide the direction of the company, and everyone down to the janitors and engineers follow those orders. If you aren't a manager, you have less responsibility and thus less power to decide or give feedback to the overall health of the business.
In America, engineers often have more input to their superiors. In fact it isn't uncommon for engineers to assume management positions in American large corporations. I would even argue a manager with an engineering background will preform better than just a manager with an MBA. But even the lowly intern is allowed to speak up to his superiors because discussion even if it is against management's wishes is valued.
This isn't true in Japan. The path to "nobility" in Japan is to work (study) your way to the most reputable university out of high school to give yourself the best chance at entering the most reputable firms in Japan.
This is why schools like Keio that are an all inclusive program for children from primary school all the way through university are so popular (for Americans, this system nearly guarantees children entry to Keio University which is to Japanese a sort of Ivy league school). They're trusted to give their students the best possible outcomes in structured Japanese society because they're reputable.
So while you may delude yourself into thinking that Japan is egalitarian, it is anything but. It is a mixture of meritocracy to a certain point with old feudal caste style concepts mixed in.
> But what if the market is set up in a way that both salaries are roughly equalized? This is somewhat how the Japanese salary system works, and I believe this is The Better Way.
This isn't the better way. This is a tendency towards socialism. Not that I disagree with the socialist philosophy. In many ways I wish America was more like Europe. But from what I have seen in Japan, this mentality allows for the idea of 仕方ない (shikata ga nai) or status quo mentality.
That is most Japanese have the idea that they can't effect change within society because that's just the way things have always been done and that's just how it is. Contrast this with America's acceptance and encouragement to change and create changes. This difference is the reason why America has continued to last as it has for so long in addition to coming to dominating the world even when large industries have been off-shored.
There are some downsides to America's behavior. Notably we don't preserve traditions and culture. But at the same time this allows for innovation. It attracts the best and brightest in the world because that's the promise: you can do what you need to change the world and that glory will forever belong to your name as long as books and information continue to be preserved.
For example Japan has had a number of major visionaries, business men, and inventors but most of them are not respected within Japanese society because they didn't fit in. The most recent being Shuji Nakamura (Nobel prize winner for blue LED manufacturing discovery) who was Japanese but has since nationalized to America. Nakamura sued his previous Japanese employer over compensation for his discovery which was a mere 20,000 yen (~$200 USD) at the time. If that's the reward for advancing society, then nobody will want to attempt to do the impossible. Instead everyone will just throw their hands up and demote themselves to the easiest and most stable work possible which is exactly what you're seeing in Japan these days. But they have another option: immigrate to America where they will be respected.
It is sad to say but I believe if Japan continues on the trend they are on right now, they will continue to sink into irrelevancy. Japanese citizens are not trained to be specialized, they're trained to fit into society. Those that fit in the best and devote themselves to the structured nature of Japan are best respected. Those that find other ways or do not follow the traditional path (the Japanese version of the corporate ladder) are not respected. So when a serious problem in Japan arises, if the leaders do not recognize it, and have the correct solution, the entire ship sinks. Because only the leaders are in the position to effect change. Not the janitors. Not the engineers.
Finally a recent popular drama that aired in Japan was Hanzawa Naoki. (Spoiler alert) In the drama, the main protagonist spends his time ethically climbing the ranks of a large national bank in order to exact his revenge on a board member of the bank that he believes caused his father to commit suicide. He's successful but in the end, he's demoted from his current rank and transferred out of the main branch (because he forced the board member to kneel down and apologize in the most humiliating way during a board meeting). When I asked my Japanese friend what she thought of the drama's ending, she just replied, "that's just how it is." She didn't bother to think for once if a better outcome was possible.