If this "feature" of Bitcoin, the ability of its users to pay money in exchange for everybody to store their data forever, is a fundemental unsolvable property of the blockchain (in other words, if future-proof methods of encoding data in the chain exist), then you have no choice in the matter - to participate as a full client in the Bitcoin network, you'll have to store this data. I wonder if this is (yet another) Tragedy of the Commons situation ...
The minimal storage burden for being a full client in a fully optimized Bitcoin network is to store all unspent transactions (and only the unspent outputs thereof), which is a very small fraction of the total blockchain size, which grows only in proportion to coin ownership becoming "fragmented" (i.e. the total number of unique bitcoin addresses possessing coins). Any storage beyond that is consumed merely to cryptographically vouch for the integrity of that first data set.
The only reason to store the entire transaction history is to favor of some highly conservative security assumptions that are important for the proof of concept, but which are impractical to the point of ridicule. If 85% of the block chain file exists solely for the benefit of the client's ability to verify the block chain isn't tampered with, and I am able to download a block chain digest 15% of the size and there is some other way for me to establish the accuracy/veracity of the unspent transaction set it represents, and my user experience is all the same, I'm likely to opt for the latter.
Imagine if online banking had two options, http and https, and using https required you to wait 8 hours each time you wanted to use online banking. Nobody would use it. People would just bank offline, or take their chances on getting attacked.
Nor is anyone going to ever download the block chain - EVER - when it gets to, say 100GB+, other than self-appointed historians who want to make sure the original block chain never dies. Everyone else not using a hosted service will be downloading pruned or digested block chains. As the block chain size tends to infinity, the number of volunteer historians will tend to zero.
If only a dwindling number of historians will download the block chain when it gets so big, you're back to the same problem as square one: you're depending on volunteers to do your backups for you. You may as well let your volunteers back up your data directly via http, so they are only backing up data they have a stake in (something they might actually do out of prudence), rather than every gig of everybody's data who mistakenly thinks the block chain is their own personal closet, toilet, and dumping ground.