"Cash is in the bank being lent out to others."

Yes, in your textbook it is. In reality, in 2016, banks are hoarding that cash outright, or "lending" it to other banks, etc., for near-zero returns.

Considering many central banks are moving towards zero or negative interest rates there's a significant cost to hoarding cash. But as you say it is a good strategy for individuals, it's not a good universal strategy - see https://en.wikipedia.org/wiki/Paradox_of_thrift