> It makes new grad applications slightly better than a random lottery
Your second assertion indicates that your first may not be true...
Even new college grads know people, have been through internships, and have the ability to research jobs and companies to find a better way in. Do that.
Ever been to a trade show? In a tight job market it's not uncommon for a good chunk of the attendees to be carrying CVs and asking about jobs. I used to roll my eyes at that, but now I see it as a go-getter getting-their-go-on, and if I were hiring for what they're looking for, I'd shepherd their app though the process and ensure they made it to the post-screen interview stage.
That's just one example of how to do it - there are tons of others. The point is that straight out of college, your job is getting a job. Spend 40 hours/week on it. Work hard. Try new things. Learn what works and what doesn't (pro-tip - every time you make it past the first stage, ask someone how you got there!). The people that do this are going to go farther than the people who shotgun 500 job applications then give up.
is there a legal restriction? i'd pay $5 to a company when applying to an actually interesting position if they promised i'd get a non-form letter from a human back about my application, good or bad.