It's not about ownership of the moment, it's about mementos that help to trigger memories (and emotions).
It's just symbolism.

If I had a shirt on the wall with Henry's signature it would do many things
- Remind me of my love for him (which would bring me joy)
- Remind me of the time I actually met him (see above)
- Bring me joy from bragging to friends etc

The signature represents the level of fanaticism I have for a particular person, whether that be natural or healthy or not is another thing.

Each to their own, perhaps you don't have the same romantic streak as me, but when Henry returned to score against Leeds I dead set cried. Tears ran down my face.