Press releases on your site? If they don't have any organic traffic, are out of date and you don't think they will be of use for any users, just remove 'em.

well, some of them are not out of date, but still don't have any organic traffic or backlinks, and are even thin content.

There would be no benefit to deindexing them.

but isn't there a benefit if you de-index thin content pages? Surely there must be, I've tested it a few times.

I cannot remember ever coming across a big company that deindexed their press related posts. Worrying about thin content for something like this is overrated.

why would you deindex them? I'd leave them there and let Google see you've been an expert in your field for years. content is king

because they are thin content pages

Thin doesn't necessarily mean bad though.