For Linux/public open source, what you said is right about 2). Once the patch is visible to anyone, it's trivial to identify exploits for unpatched systems. But 1) is still a valid use-case for embargoes for Linux vulns, right? Like, if this patch had taken a few weeks to develop before being confirmed working and published, that's potentially valid grounds for not sharing details during that time (within reason), no?
Usually, nobody even bothers to check. LPEs like this are too common to even categorise effectively.