The only way to relieve the number of fish taken out of a river in one day is to limit the number of days it is open. When you have an umlimited supply of fisherman and a limited supply of fish, it is a no brainer. The amount of fish to get taken in a day will not change until there are no more lines in the water.

As long as there are empty tags on the water, you have done nothing to slow the harvest rate by making it a 1 fish limit.