I don't know how well it makes sense to create a different birthday or wedding gift campaign off of Bitcoin but it makes more sense to gift Bitcoin directly to someone instead of still turning it to a physical present of any kind. @OP, if you want to gift any distance relative or love one a birthday or wedding present, you can simply send them Bitcoin. It will highly be be regarded as a good gift if the person knows about Bitcoin, but even if the person doesn't know, when they see the value of the coin, they will definitely appreciate it.
Yes gifting items like physical bitcoins for example are also a great way to give bitcoin to someone that maybe doesn't know exactly how it works or even has a bitcoin address as well. The whole process here of reaching out to them or having them set up a bitcoin QR code for a wedding or something is definitely a great idea though, results definitely may vary though. I would honestly expect to see more types of those posts on social media advertised like a go fund me page or something.