That means banks have to keep a larger portion of their cash on deposit instead of loaning it to clients, thus restricting the flow of money into the economy.
Banks use the time frame as a filter: if you can get by without your deposit for the better part of a month, they can see that you have the cash flow to properly rebuild your credit.
What's more, a European fund would not have to be big enough to deal with simultaneous deposit runs across all of Europe but only with ones in the periphery, since money would presumably flow to banks in core countries such as Germany.