You might have been doing that, as was I, but a lot of people were not - and their flimsy bags were ending up as litter. This is what this policy is designed to prevent.
So what were they doing? Not lining their garbage bins? I find that unlikely. They were most likely buying plastic liners (ie. bags). In that case, the smart thing to do is to get them to switch to reusing their plastic bags, not making it harder for people who already reuse plastic bags to get bags.
>and their flimsy bags were ending up as litter
I'm not convinced that any meaningful amount of plastic bags end up as litter. They're used to transport something, typically to someone's home, where there's easy access to a garbage bin.
They were already buying bin liners to use at home. When bags were seen as disposable they were often put in public litter bins (where they do not always stay, in busy areas with full bins) or simply discarded in the open environment. Anecdotally there seems to be much less of this going on now and the relatively common sight of Tesco carrier bags (other supermarkets are also available, but these seemed to be the worst offender) blowing down the street or caught in trees seems to have largely disappeared from what I have seen since this policy was introduced. There is still litter of course, but the most noticeable litter is now food wrappers rather than plastic bags.
