Isn't finding a new job a recommendation problem, and don't we have enough real-world systems doing the same thing? Ideally, I would like to inform the system of my preference, and let the system do the heavy lifting of finding and applying for the job.
If a platform makes it very easy for people to apply for jobs, and very easy for jobs to be advertised, but is not good at matching and filtering the number of possible matches to a small number of high-quality matches, then both employers and prospective employees may get flooded with a large number of low-quality matches that have zero or a very low chance of resulting in a deal that is agreeable to both parties. That doesn't really help anyone.
From an employer's perspective, perhaps what they want is identifying some channel or way of addressing and reaching a particular sub-population* of applicants who are more likely than other populations to be a good fit, to make their hiring process more efficient. Would you prefer to get 1000 applications for a role, where each person is 1% likely to be a great fit, or 10 applications for a role, where each person is 30% likely to be a great fit? In the former situation you expect to have 10 great candidates, and in the latter situation you only expect to have 3 great candidates, but the latter situation requires one or two orders of magnitude less money and effort to process the applications. Similarly from the perspective of someone looking for a job. Maybe it's something of a marketing and statistics puzzle for both parties.
It may not be an advantage to either party to participate in a large central marketplace that makes it harder to differentiate themselves from their competitors, as it commodifies both sides to some extent.
* i mean "population" in the statistical sense.
One immediate problem is that some job applications could create ethical or social conflict problems. For instance, it could apply at the company you already work for, which you might think is easy to prevent, but it would be hard to prevent you from applying to subsidiaries, vendors you work closely with, etc.
At the very least the system would have to let you opt-out of applications.
I got let go by one company that had a very strange severance agreement that said I could be sued if I ever applied to work for them again!
I've spent years and countless hours doing research in this space. Happy to knowledge share and discuss the subject if you're interested.