There are two environmental issues going on:
1) The energy used to make the bag
2) The trash impact of having the bag end up outside the normal waste stream (i.e. in rivers and oceans)

Plastic bag bans are actually a negative for #1 since the thin bags are far more energy and resource efficient than alternatives (even reusables which often required 10x to 100x more energy than a thin bag)

For #2, reusable bags are a positive and this is the main reason why the bag bans are in effect.