More savings = more loans is old fashioned banking. Modern banks only care about the capital requirements they have to meet. It doesn't matter how much people are saving
That's true in theory, but banks still aren't lending to the extent that would otherwise be expected. My theory is that a larger margin of money to work with could improve that; no point in being so difficult on businesses wanting loans if you've got so much more cash to play around with anyway.
If you really wanted more saving, better solution would be to make high-yield CDs tax deductible, so people have more incentive to store their money and banks have more incentive to chase after savers with good rate offers.
That would be an issue for Congress though. Even if Fed board members did want to encourage spending, the politicians probably would not. They'd have to work with the resources they have.