I thought the majority of the hundreds of gigabytes consisted of dormant and throwaway addresses that still have some value on them, but it sounds like I've got the wrong impression and by removing transaction history for empty addresses and other historic block data, it's only a few gigabytes?
The need to track previously used stuff in some other systems to prevent transaction replay is a design flaw that Bitcoin avoided.
The vast majority of the blockchain data is digital signatures which you don't need anymore once you've validated them (except to help other people sync up).