Since very few types of plastic are actually recyclable most of it ends up being burned despite being separately collected, so I don't think you can simply discount the recycled plastic from the plastic waste being produced.

Japan burns about half of its collected plastic via thermal recycling (recovering the energy) and recycles about a third into new products.

The key point is that Japan recycles 85% of its plastic waste, which is excellent compared with a country like the US that recycles about 10%. And, the per capita plastic use in the US is far more than in Japan.

This whole point pops up on the internet so frequently because tourists go to Japan and see lots of individually packaged items in supermarkets and convenience stores. Yes, there is room for improvement there, but overall the situation is not as bad as many countries and probably doesn't deserve the attention it gets.