You're right, unfortunately the majority of plastic bags sold/given away (in the UK but I assume everywhere) are single use cheap plastic bags. They end up being used as bin liners and sitting in land fills for hundreds of years.
The real problem is how to get the microbes to function in landfills so that the contents can degrade at a faster rate.
Then you've got the problem of stopping secondary effects in landfills such as water seepage. What happens if high concentrations of these microbes start dissolving plastic water pipes? We could replace one mistake with another.
There is a long way to go but the kids made a good start. Ultimately we just need to stop using plastic bags.
The way they've pretty much solved the plastic bag problem here (Austria) by charging for them. Result: ~99% of people bring (and reuse) their own shopping bags/baskets.
There are various incentives given by the UK supermarkets for using your own bags (IIRC, Tesco: "green" points, Sainsbury's: 1p/bag saved off your shopping, may have changed since I moved away from London) but they've got them the wrong way around, as there's no penalty for carrying on as before. If people start getting charged extra, a lot more will switch to using their own bags. With only positive incentive, my gf and I were the only people we ever saw who used their own bags.
The Austrian solution only applies to supermarkets, so other kinds of stores still hand out free bags, although I suppose supermarkets are (were) probably by far the biggest source of bags.