>if Greeks had easy access to large & stable foreign banks they wouldn't need to worry about the sorry state of Greece's own banks
Trouble is that's not so. If people just stopped using Greece's banks they'd go bust and then either the government would have to bail them out or savers would lose their money.
As to why have a local banking business, the bulk of useful banking is lending to local businesses and people getting houses so there's a benefit to being local so you know the people, businesses and houses. Of course it needs to be regulated so they don't take your savings and punt it on dumb stuff.
Trouble is that's not so. If people just stopped using Greece's banks they'd go bust and then either the government would have to bail them out or savers would lose their money.
As to why have a local banking business, the bulk of useful banking is lending to local businesses and people getting houses so there's a benefit to being local so you know the people, businesses and houses. Of course it needs to be regulated so they don't take your savings and punt it on dumb stuff.