This is something that the protocol is designed to handle via changes later. Once transaction registers get too long, the database itself will no longer be hosted entirely on each macine in the network and will instead be distributed (with plenty of redundancy) full database nodes will still exist but will not be nearly as common as it is now. As the network grows, the protocol can be modified to allow normal nodes to carry half the database, then 1/4, then 1/8th, and so on. The larger number of nodes will allow smaller portions of an ever-larger database to be carried on each node without risk of loss.
That sounds promising. However, I've read stories that Bitcoin mining takes a lot of energy. If we can wring more redundancy out, that saves everyone money and makes it more attractive to run a server node. Besides my ideas are based on simple quality control models. In a factory, you don't have everyone inspect every widget, you do random sampling.