With any knowledge worker job posting, there are hundreds of perfectly qualified candidates, maybe thousands. The knowledge taught at Harvard is already disseminated. You don't learn anything different with an undergraduate degree at Harvard than you would with a degree at directional state. The difference is now you know professor X, who lets you work on his super cool project Y, then employer Z sees you did project Y with well known professor X, who wrote a letter with nothing but high praise of your intimate accomplishments on project Y and why you are therefore extremely qualified, and you get a great job.

To break the system would be to snap your fingers and will more knowledge worker jobs into existence to meet the oversupply of qualified candidates, but given our free market society and increasing disfavor of public engineering and public research, that just isn't ever going to happen. So you try and play the game as it is the best you can, and apply to schools like Harvard with faculty who can push your life forward.

In a world of imperfect information, how do you prove to a stranger that you are knowledgable, in less than a full day of interaction?

That remains the problem, and credentials/prestige remain our best way of dealing with it. In other fields you develop portfolios (e.g. github repos) perhaps that's what education will evolve to, developing a student work portfolio to prove you are knowledgable.