I'd be happy to write a carefully crafted, specifically tailored cover letter when recruiters are willing to respond with a detailed, individualized rejection letter.
The thing is, it’s not symmetric. They have far more to lose by leaking specifics than you do. The most efficient cover letter conveys just how little initiation you will need to conform to company values. You should edit this down, but by no means do all the typing. The median rejection letter gets the same treatment.
No, it's not symmetric, but not at all in the way you describe.
Worst case, from the employer's side, is they might have to pay the successful candidate *gasp* a few tens of thousands more per year (out of a budget, in a huge percentage of cases, in the two-to-three-digit millions or higher).
Worst case, from the employee's side, is that they might not get any job. For months. During which they still have to pay for food, rent/mortgage, clothing, utilities, etc, possibly for several people.
And these days, the median rejection letter is none. Most employers just ghost prospective employees who didn't make the cut.
The worst case on the side of hiring is facing a lawsuit because you treated candidates unevenly. And the detail you go into about a candidate are too personal for the hiring process.
So you might have to pay some legal fees, and possibly a fine.
That's still not symmetrical in the common case. It's incredibly unlikely that such a thing would lead to a business going under, while it's all too likely for a job-seeker to have to spend months looking for a job, with no income, very little savings (because a huge percentage of Americans simply don't make enough money to save any even if they have jobs), and a horribly dysfunctional social safety net.