Only if that job board was an actually useful and common source for genuine hiring. If it becomes “these companies are checking a box, don’t bother applying” or “these companies are considering an H1-B application, flood them with resumes”, neither of those is helpful to qualified workers who actually want to find a job.
Agreed. I don't really know how the current process works, but I would assume there is some level of oversight, meaning that errant (unqualified) applicants shouldn't detract from a qualified h1b under the current system any more than a centralized one. Tying a profile to a human (gov can do this) should at least help with determining whether an applicant is qualified (not that they are an actual fit for the team) which could provide some proxy for fitness of the current pool.