Correct. Producing new coins is a side effect of mining in POW systems in order to help pay the miners. For bitcoin specifically, once the reward falls below t

Correct. Producing new coins is a side effect of mining in POW systems in order to help pay the miners. For bitcoin specifically, once the reward falls below the Satoshi, the entire cost of mining will fall on the shoulders of users in the form of transaction fees. This will not work very well.