It's all gone pretty smooth except for grocery delivery services. Instead of using one time use thin plastic bags, they now have to use reusable bags. That they never reuse. So places like our company that get office foodstuffs delivered weekly, end up throwing away stacks of thick plastic bags.
Apparently though the legislature is working on a fix for this.
What's worse is that they're harder to reuse. Since they aren't resistant to water, there are fewer other uses that they are good for.
Businesses are far and away the biggest offenders when it comes to waste in general and particularly plastic waste. Getting individuals using reusable bags is fine but really doesn't address the biggest offenders.
In terms of plastic use the reusable bags are much better. It doesn’t take too many reuses before a reusable bag is a net benefit. Compared to other energy uses the plastic bags are a tiny amount so I don’t worry too much about that.
According to this Danish study a cotton bag has to be reused over 7k times.
Most of the reusable bags in grocery stores are polypropylene, and those you only have to reuse 37 times. So that is better.
When I’ve been in Europe I’ve often seen that there are no bags except for fully re-usable tote bags that you have to pay 1-2€ for. It really only takes one instance of forgetting your own bags to teach the lesson.