Very true I think. When the banks started to fold in the UK I split my cash into units of up to £35000 each into different banks. The guarantee was per institution, not individual. It certainly made more sense to me to fit within the guarantee limits, though there was no absolute guarantee that even those limits would hold.
Per person depositing in an institution. On European level, it would be futile to try to limit it to EUR100k per person, for many reasons, for instance because lots of people can have multiple identities -- expect perhaps in the Big Brother societies in the northern EU countries, where you can actually do a census by saying SELECT COUNT(id) FROM population WHERE alive=1;
Moreover, how would you treat accounts that are not owned by a person, but e.g. companies?