Plastic does take a long time to decompose, but to the extent this is actually a major issue isn't clear to me. A plastic bag takes 20-40 years to decompose per the BBC. That landfill you use will be there long after we're dead, certainly more than 20-40 years.
The main issue is whether it makes it to the landfill in the first place, but this isn't particular to plastic. .
The main issue is whether it makes it to the landfill in the first place, but this isn't particular to plastic. .