I'm not sure what other solutions look like: Gatekeeping of various forms including institutions and certifications, letters of introduction like essentially the US service academies, standardized tests, informal networks, etc.

There's two distinct reasons why more qualified candidates might get skipped over:

1) There is too much noise occluding their signal.

2) There is a form of gatekeeping going on.

Gatekeeping only really works in exploitative systems (e.g. "me and my children are the masters, and you and your children are the slaves") or when the noise is so high that companies wouldn't gain much from not gatekeeping (e.g. Harvard admissions in the late 1800s).

So, if you don't exist in an exploitative system, providing more signal is going to both benefit deserving candidates and punish gatekeeping companies. I don't see why a reputation score would increase gatekeeping.

At the end of the day, every applicant could be ranked on their ability at the job. Wouldn't it be best for everyone—companies and prospective employees—to know where they rank up, so they don't waste time applying to hundreds of jobs or sifting through hundreds of applications?

The only people who are hurt are the hustlers: people who spend far more time hustling for a position than gaining the skills needed to do well in that position. Their goal is the extreme limit of noise, where success rate is directly proportional to how many applications are filled out, and I have no sympathy for the destruction of the commons (that I have to live in).

For a lot of things, hustling is probably at least as important to me as a hiring manager as rather amorphous "skills needed to do well in that position" at least as an entry-level employee. Of course, I don't want someone who has none of the skills needed for the job in most cases but they probably don't know most of what they need to learn anyway.