Because it's hard to match a visual depiction of the bike and owner to a printed receipt.

Why would you want to repeatedly 'interact' with that any more?

For one thing, it's common for enthusiasts to replace stock components. A serial number stamped onto the frame isn't useful all the time, especially if the frame itself is secondhand. If someone takes your >$2,000 carbon wheelset then you're SOL, likely no matter what.

Why not just keep a searchable note of it in a notes app?