You did open yerself up to that one, Hermann!
I think some folks do it because their name and their nick don't match. Some folks add their real live name.
To some of us who've worked in an office setting for decades, it's just automatic. I worked for the government and learned that if you didn't make everything crystal clear, the deadwood in the office would arrive in their clown car, all in a lather of anxiety. I have distintive handwriting yet unless I signed every scrap of paper I wanted them to read, it created confusion among the dumber ranks.
For those of us that were born pre-internet, signing our writing is automatic. We used to actually sit down and **gasp** write letters that were sent snail mail. You signed those. Period. There was no thought of sending off a letter without signing off. Part of that is courtesy, part is following an old protocol, and part is owning our words.
Even now when I leave a note for Shell, I sign it. We are the only two in the house that can read. (Our Jack Russell is smart, but not quite able to read. Yet. She can spell.) Who else would be leaving her a note that says, "Sweetie, I've gone to walk the dog"? But it's always signed.
When you sign something, you own it. You're responsible for that string of words out there floating around the world. Thoughts, ideas, creative endeavours ... they are all children of our intelligence. Most of us sign them to give them roots in a system that will support them if challenged.
Probably a bit more existential than you were looking for, eh? Forgive me ... I'm still drinking my first coffee of the day.