I quit my job recently and my last day is next week. Today they emailed me a separation agreement and asked me to sign it. It basically makes it so I can't sue them - I was just wondering, why would I sign it? I've been paid for the last days that I'm working, so signing it basically removes my rights for no benefit. This is in the United States.
I normally don't sign anything unless there's a benefit for me to do so. If they're offering compensation in return for indemnification, I'd think about it. But other than that, there's no way I'd ever agree to that.
I mostly agree with your question. Why would you sign it? The only reason that it might burn a bridge if you want to use them as a reference, i.e. they could be motivated to say something negative if asked. A simple and legal example is "We wouldn't hire him again and that's all I'm able to say" and that could torpedo a job that had someone ask them that question.
If the place wasn't terrible, that might be enough make me consider signing it. If the company did anything improper (like sexual harassment or discrimination, even if I didn't complain) then I wouldn't.
I would also ask your boss and/or HR why they want you to sign it. Personally, I've never heard of such a thing.
There is no reason you should sign it unless doing so benefits you.
Once I leave a company (get paid in full) I just ignore any and all correspondence that doesn't involve me making something more out of them, whether I left on good terms or not. Ignoring is better than refusing, it leaves your options open. And it leaves the ball in their court to follow up if they really want something badly, in which case they need to make it interesting.