- If you install such keys to a host, and an attacker (with access to said host) has catalogued your ssh keys, they can see that you have access to said host (if they can correlate your method of publishing the keys to your identity)
On the other hand, if you go to the other extreme (?), you can have a different public ssh key per host. This way the server owner/attacker is not able to correlate that ssh key with other keys to recover your identity. (You need to take care that ssh won't offer too many public keys in that case.) Example case of a service that might get offered many ssh keys: github.
Personally I don't bother. But I wouldn't be too bothered about just putting my public keys to some "secret" URL in the internet either, so I can easily enable myself ssh access to a host with a single curl.. Maybe I should indeed do that.
A single Security Key can authenticate to Facebook as WeedLover420 and then be used to sign into the Google account of the Secretary of the US Marijuana Task Force and even if both Facebook and Google were co-operating in the work there's no way to connect these authentications. Obviously WeedLover420 is more likely to get caught because they used the same IP address to do both things and they stink of weed and they look stoned all the time, but none of those are because of the Security Key, that was locked down good.