Checking your serial number isn't just about record-keeping; it provides critical data about the hardware that isn't always visible:

The serial number checker, therefore, serves as a sorting hat. It separates the pristine collectors' items from the tinkerers' toys.

: Serial numbers are unique identifiers used to verify ownership or recover an NNID (Nintendo Network ID) if a system is lost or stolen. Where to Find Your 3DS Serial Number

The first layer of serial number checking has nothing to do with bans and everything to do with authenticity. Because the 3DS is a legacy console, the market is flooded with replacement shells, frankenstein consoles (units made from the parts of broken devices), and counterfeits. Websites like 3ds.guide and various community-maintained wikis host databases that decode the serial number.