| Alternatively, wait a few hundred years until you need several hundred terabytes to store the blockchain, which is required for transactions. That's going to be a problem.
It seems more likely to me that in a few hundred years, several hundred terabytes will come in your mobile implant than for hundreds of terabytes to be a storage problem.
There is a limit on information to area in space. Eventually, bitcoin is going to be impractical to store even if you have a very large storage device at absolute maximum capacity.
The blockchain length is only growing linearly with time, but that's because it can only process O(1) transactions per hour. It'd be growing exponentially if either the monetary velocity or the size of the real economy was growing exponentially.
It seems more likely to me that in a few hundred years, several hundred terabytes will come in your mobile implant than for hundreds of terabytes to be a storage problem.