Especially in today's world, the amount of cash in the system is relatively irrelevant to the concept of money supply. We use electronic transactions for so many things that the amount of cash compared to the amount of liquid money is really quite small. So I would say you should not think about cash in this context.
When banks create money, they really create money. When I deposit my money and they loan some of it out to you, there is more liquid money than there was before they loaned it to you. It is not just recycled.
If I deposit $1000 from a paycheck and $900 of it gets loaned to you, where did that $900 come from? It's not coming out of my money because I still have $1000 in the bank. It's not coming out of the money that anyone else has -- the loan to you does not decrease the balance in the account of any other depositor.
So you can't say it's recycled -- it is new money created by the loan.
The actual physical cash is, of course, recycled. And banks don't create physical cash. But they do creat money.