(When) does the age of my loyalty card matter?

Are there any major loyalty accounts where the age of the loyalty account matters? I was thinking that this might matter for things like targeted offers, I'm not sure.

I ask because, in some cases, I might want to create a second loyalty account so that I can link that to other apps and not worry (as much) about accidentally granting sensitive information to a malicious actor (like my presciption history or something like that).