Cork can be grown and harvested sustainably, as long as there are enough trees (which live ~300 years) to meet demand (cork is bark harvested like shearing sheep).
We produce 380M tons of plastic per year. IIUC, that's about the size of the entire lumber industry - of which cork is a very small insignificant percentage.
Cork has a very small part of the planet where it grows well, and basically everything else valuable grows well there, too...
The Nanocrystalline Cellulose market will be bigger than cork by 2030 probably - and even that is 25 years away from making a real dent in plastic consumption (aggressively).
It's orders of magnitude away from even taking out 1%.
Any material looking to fulfill that demand will start from that position; why would anyone be producing the material if they didn't already have that market? Every new thing starts from zero; plastics were at zero too, at one time.
It's not a new market.
But there are risks: https://apsjournals.apsnet.org/doi/10.1094/PDIS-03-16-0408-F...
Another interesting option in this realm is mycelium, which could be better scaled on an industrial level.
I, for one, welcome our industrial biological process overlords.
Especially in the cases where it supplants the more traditional kind that often involves lots of animal cruelty. I have no intrinsic objection to eating steak from a disembodied vat-muscle.