My (very uninformed) guess is that this is cultural. When democracy spread, Europe already had a good system of tracking people. The church was keeping records

My (very uninformed) guess is that this is cultural. When democracy spread, Europe already had a good system of tracking people. The church was keeping records of every family for hundreds of years already. In contrast, the USA is a country of immigrants where new people without a history came in all the time. Tracking who votes where could not rely on an established system.