Job openings are usually filled internally first, before they even go out to the public. Here in the UK I believe its law to actually post it regardless of whether it has already been filled internally.
Jobs being posted even though there is a person internally that will get the job with 99% chance anyway is a problem that does also occur outside the UK. This shows that legally enforcing a job posting does not help much. In fact, these situations were a major motivation for thinking about solving the problem using cryptography.
Using the Blockchain or other solutions might be interesting though, I've never really thought about it being involved in the application process. Personally, I'm not a massive fan of how applications work anyway, with companies now looking to diverse employees, there's probably going to be a lot of bias involved regardless of the way its implemented. Also, while you may come up with a solution that works quite well, convincing recruiters that they don't need access to the entirety of the persons background, skills, and personal details would be difficult, when they can right now legally ask for that.
In cases where there was a legal requirement to post the job offer in the first place, it may be possible to increase the pressure once there is a working system in place. No doubt that recruiters who want to fill the position internally would be opposed to a system that makes it harder for them to do so. Right now, they can always say "well, but this person matched our requirements so much better than all the other candidates", and it will be hard to prove that it was a subjective decision. But if recruiters who don't need that are able to prove that their decision process was fair using publicly verifiable blinded information, other recruiters might have it harder to defend their less transparent process.
