"School" is quite variable.
Weak signal: you only went to class and did OK in them.
Strong signal: you had an internship, or undergrad research experience, or part-time employment as a TA/tutor, or have a completed project to show off, or some kind of non-trivial community/group/club/fraternity leadership.
Really strong signal: you published a paper with someone I know and they recommend you to me.
Most people are looking at whether you just went to (whatever they consider) a top tier university.
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).
On the flipside I'm not finding good resources to find startups to apply to that don't have hundreds of applicants already. There's no good answer the market has come up with as far as I can tell, so everything just gets worse for everyone as a result.
University admissions has followed a similar trend, going from 5–10 being "spray and pray" twenty years ago to 20–30 applications nowadays. However, it didn't increase as much because (1) each application costs money, and (2) most universities expect a cover letter. It still costs quite a bit to filter the applicants, but the fee helps pay for that.