Would this destroy Bitcoin? No, it would not;
If changes in usage resulted in centralization of validation it would 'destroy' Bitcoin. No, it wouldn't stop existing— but it would stop having a point. We have other ways to have centralized money and Bitcoin isn't an especially efficient one.
However…
I think it would be a huge loss. Why? Because the never-ending-supply of skeptics learning about Bitcoin can no longer trust solely in math and cryptography to audit the system. As soon as you start deleting information that is "no-longer useful" you have to start trusting the mining community that nothing dubious has been done though the probability of a mining conspiracy is extremely low;
Technology like pruning and txout trees are things which _prevent_ centralization. What you're saying above right now applies much more strongly to block validation then they do to storage. Storage has been growing at a rate faster than moore's law and slow nearline storage is very inexpensive. At home I already have enough storage for about 100 years of the current maximum blockchain growth. But timely validation is much more costly and there is a risk of a tragedy of the commons on performing it and everyone moving to centeralized webwallets or lite nodes that trust other nodes to be honest. Technologies that minimize the cost of fully validating nodes are not a threat, they are potentially a salvation.
(In particular: it's already trivial to mine without having the history— all of these centralized pool miners are doing so already, and unless you're using P2Pool, bitpenny, eligius-gmp, or solo mining you are guilty of it too, so these improvements don't create new ways of being anti-social)
I'm not too worried about your concern because the cost of storage is reasonably cheap, and preservation of the data is valuable for many reasons and not just preserving the autonomous trust-freeness of the system— e.g. historical, contractual, investigative, and academic reasons. But the autonomous validation is probably enough incentive alone, after all the whole Bitcoin system was created in order to have that property.
In addition to that it's possible to retain strong confidence of trustworthyness in even in an environment where many people don't have access to the long ago historical data— I suggested an idea I call "proof of treachery" on the Bitcoin-dev list:
If the rules are violated in a chain someone who observes the violation can copy out the minimum necessary data to _PROVE_ that a violation happened (which is always small: it's no more than two conflicting transactions or one bad-signature transaction, and the hash trees that connect them to the header) they can then broadcast these proofs and any node— even one without the history can see and understand the proof just on a purely 'mathematical' basis— without trust and then completely reject any chain following the point of treachery, even if that point was long before the history they have. Because information is hard to stifle so long as there was at least _one_ honest node that observed the cheating it would be reliably defeated. That is not quite as good as "you checked for yourself", but Bitcoin doesn't quite achieve that even with access to the whole history because someone could have potentially concealed an alternative history from you (e.g. there is another longer chain but no one has told you about it) so Bitcoin's autonomy already depends on it being too hard to effectively conceal the truth from nodes for too long. Plus, a proof of treachery is much smaller and more easily passed than a block (and it's origin more easily concealed from someone who would want to suppress it).
So I think so long as we build all these paranoid little tools that preserve the vision of Bitcoin and act with thoughtfulness and care when making adjustments to improve scalability which might result in centralization then Bitcoin will do just fine.
