Personal computing will definitely scale to meet the demands of running a full node. And even if it doesn't, server storage is there. Right now you can get a petabyte of storage for less than $100k.
As for there being a practical solution, there might be a need to prune some of the blockchain and archive it at some point, but right now we don't have to worry all that much. Chances are, though, that personal computers will continue to grow in storage space and we won't have to worry about running out of space. It'll just more come down to the time spent.
The blockchain itself
cannot be pruned.
But since Bitcoin Core 0.11.0, you can prune the blockchain database you have stored (basically automatically remove older blocks after a certain size).
This defeats the purpose of running a full node, because you're not serving historical blocks and therefore not participating in network health.