They can't see number of days spent, due to GDPR. In some countries even provinces don't exchange that information with one another, let alone countries. Withdrawn residence permits stay valid for all countries except those who originally issued them i.e. can still be used for entry and exit through all other Schengen countries until their validity dates expire. This is a mess. I travel with two nationalities and 3 residence permits issued by 3 EU countries, and if it was coordinated i'd have a hard time explaining myself every damn trip, in reality, no one gives a damn. If EU countries believe they don't have a problem of illegal immigration on the scale US does perhaps this is simply because they don't know.