I think it's a great idea.
The environment is just ever so slightly more important than a little bit of inconvenience for shoppers. (Not that charging for plastic bags isn't going to ensure that this planet is habitable for human beings in 50 years, but it's a step in the right direction.)
It's a crying shame that the environmental message seems to have got lost, people seem to have forgotten about it. (It's a bit 1990s really, IYKWIM).
I'm just of guilty of this by the way!
However the reality is that it's getting ever more urgent.
My personal opinion is that people find the "save the planet" as bit abstract. The planet is a big thing! And actually, very unlikely to disappear any time soon.
I think a better slogan would be "save the human", as what we're talking about is the survival of the human race on this planet. For much of the history of Earth, we wouldn't have been able to survive here as the conditions would have been too harsh. The mild weather for the last few millennia has allowed the human race to survive and flourish. If the weather systems heat and/or become chaotic, we're fucked. It's becoming a very real possibility (there's mounting evidence and very few serious scientists disagree about the reality of climate change these days).
Worrying about the inconvenience of a few plastic bags is laughable tbh. Dark, cynical, gallows humour laughter.