This situation makes up a good portion of an intro game theory course - the section is usually titled "games with asymmetric information", the problem is described as "the market for lemons", and the solution is described as "signaling devices", all of which are ridiculously un-Googlable terms, unfortunately. The economists who noticed this phenomena won a Nobel Prize for it, so there's a good indication that it's well recognized.
Also, a ridiculously amount of money is already made compensating for this, and we tend to hate the industries that make it. Consider this: almost the entire higher education industry is devoted to letting unemployed young people signal that they are, in fact, fit for the labor market despite never having held any job. The certification industry takes over that function for older workers, letting them signal that despite being out of work or wanting to switch fields, they can perform the job they're being hired for. A major portion of the open-source industry is driven by programmers who do that more directly: by writing code on their own time, not locked up by NDA, they signal future employers that they can write good code and increase their value on the open market.
Another interesting observation: one way to get rid of the problem would be to make all information public. If all of your past work products, private statements, interactions, personal beliefs, etc. were always available to anyone who wished to look, then prospective employers could always completely and thoroughly evaluate whether they wished to work with you. And vice versa: companies that act blatantly stupidly or crookedly would have their stupidity and malfeasance exposed to the world, and everyone would refuse to do business with them. It's like Foucault's Panopticon, yet instead of having a single authority watch everybody, everybody can watch everybody else.
Somehow I don't see this being politically acceptable, though.