1 block is added to the chain approximately every 10 minutes. That means at most 6MB per hour, 144 MB per day or ~52.5 GB per year. Where do you see an exponential growth here? Even if we consider Segwit, or even if the block size is further increased in the future, that's still a linear growth. I'm not sure how you came up with petabytes, with current growth we'll reach 1 terabyte in about 20 years, that means 20K years you reach 1 petabyte.
Now, even if your calculations were somehow correct, I'm not sure why that would result in centralization. Bandwidth is a much tighter limit than storage. Reaching those numbers in the near future would require a huge bandwidth. If such bandwidth would be maintainable by enough people then surely storage would be cheap enough and most people would still be able to run full nodes.
With mainstream adoption which is I assume what we are all hoping for and the replacement of fiat currencies there would be a massive amount of growth and probably millions/billions of transactions per day. This is the growth that I'm referring too.
Now, even if your calculations were somehow correct, I'm not sure why that would result in centralization. Bandwidth is a much tighter limit than storage. Reaching those numbers in the near future would require a huge bandwidth. If such bandwidth would be maintainable by enough people then surely storage would be cheap enough and most people would still be able to run full nodes.
I think bandwidth will be the limiting factor in most underdeveloped countries. Consider some parts of Africa as an example currently they are able to host full nodes however with the increase of size of the blockchain they might not be able to keep up because of the limitations that Africa put on their customers. I lived in S Africa for a while which is considered a little more developed than other parts but internet is still a serious problem there.
