I wonder if this still applies to certified compostable cups.
First of all bio-polymers is nothing new and revolutionary. The first plastics where bio-polymers like bakelite made from cellulose. The only reason we started making polymers from oil is because it's a rest product from the oil-industry and thus cheap but the inherent properties of polymers are the same whether they come from oil or plants and they typically don't break down in nature. The only positive thing with plant based polymers is that they could to some degree be considered carbon neutral.
But there seems to be a lot of misunderstanding that keeps spreading because we inherently think bio-polymers should be bio-degradable because they are made from organic material. There is one bio-based polymer in particular, PLA that is actually said to be bio-degredable and used in paper cups but this is in industrial facilities and not in nature where the degrading process is at lest 70 years under optimal circumstances.
And there are more problems with polymers then just the fact that they don't brake down in nature. They contain toxic and endocrine disrupting chemicals like BPA.