Same question was asked about the internet.
What you're asking is a scalability issue. What you need to understand is that scalability as now the past century is a never ending issue. 40 years ago the best computer had 32 KB of RAM at nearly a thousand pound sterling at the time. That's about 4900 + pounds today. Only 32 KB..
"not enough storage" is never a problem in the computing industry. Even in the cryptocurrency industry, massive headway is made to tackle scalability. Just take for example this one weird thing in the Bitcoin development scene called MimbleWimble. Once it's done and rolled out to the masses, it is mathmatically projected that transaction data size can be reduced as much as 20x. Fees will never be an issue with Bitcoin anymore.
From what I know, the fastest growing blockchain in terms of data size is Ethereum, now at 1TB. that sounds big at face value, but the full story (and why there is no need to worry) is so complex that im nowhere near qualified to explain.
As a consumer, just rest assure that this problem is dealt with by the developers and there is no need to worry about it. Because explaining why you shouldnt worry about it will go way above your head.