It really is though - carrying my own bag, which took significantly more resources to create and transport (by a factor of 100s), and which requires washing (once every 6 months or so, and yes, I can put them in with other stuff, but that's still using resource - it's not resource free.
Lets try some sums.
1 old style carrier bag (exactly like the type I buy now to line my bins) weighs 7g of plastic.
1 lidl cotton bag (hilariously with plastic coated labels declaring it to be 100% cotton) weighs 150g.
The cotton bag is bulkier, so takes up more space to carry in a container. I'd estimate that in the space I can fit one cotton bag, I can fit 8 folded plastic bags. If they were in shipping packaging, compressed together I would confidently double that.
The plastic bag has half the carrying capacity of the fabric one, so I need 3 fabric for the weekly shop or 6 plastic.
The plastic bag was made in this country, the lidl bag was made in India.
So for my shopping trip previously, I would have been transporting 42g of plastic 50miles (estimate, I know where the bag factory is) - to the shop for once, and then 20 miles home with me. Those bags would then be used as bin liners, going to landfill.
Obviously if the bags came from China this would be different, although still transporting 7g only twice (to the store, and then home) is much less resource than transporting 450g to the store, then every time you go shopping
For my shopping trip now, I transport 450g of cotton 5000 miles to get to the shop, then 40 miles for every shopping trip - there and back. Then every 6 months I run them through the washing machine - which takes 6kg, so the bags take up 1/12th of a load/soap. I do that until the bags are destroyed.
So you tell me? Is it a simple sum? Is transporting a bag that weighs 21x the weight and takes up 10x the space being shipped 5000 miles before we even begin going to be made up vs. the impact of a conventional carrier bag?
How about when we add in that everyone I know still buys bags to line their bins, where previously they re-used the carrier bags? So plastic usage for most people hasn't actually changed a lot, but non-plastic bag resource has rocketed.
Or lets talk about the people who they were targeting, who would never bring their own bag - like my ex. He just buys bags for life and chucks them, just like he took normal carrier bags and chucks them - so his environmental impact, similarly higher, as the bags for life are so much thicker.
It's not simple. Just be up front about that. Neither the bags, nor people's behaviour is simple, and pretending it is is my whole problem with the whole shebang.