With many people not wanting to carry a bag at all times and global demand rising, we're bound to see more Indonesian rainforests being clear-cut for cheap paper, and "reusable" bags with energy and resource-intensive production methods being used once or twice before being tossed in the garbage or ending up on the side of the road.
With bans on plastic bags should come regulations on actual sustainable substitutes. Require locally made paper with verified sustainable wood/recycled pulp or something similar, or we'll be facing another crisis 10 years from now.