... or, the bitcoin developers will just have to add a way of removing that data when a new block is mined, which I guess is what will eventually happen. What a mess.
As long as there is any option of storing anything user-derived in the blockchain, this problem will exist. And it is conceivable that the transaction amount can be used to encode binary data... and this doesn't just impact Bitcoin, but also normal banks. Assuming a bank with two accounts and no transfer fees, I could transfer money between the accounts and encode my data e.g. in the "cent" division, with every transaction encoding a single byte. So technically the bank is in possession of child porn (or, to choose something of lesser importance, the tiny libdvdcss code), but is simultaneously not allowed to erase it due to financial transparency laws...
As far as I know (and that ain't much -- I'm not an expert), bitcoin's fundamental contribution was solving "The Byzantine Generals' Problem"[0] in a novel way by using its proof-of-work algorithm combined with the blockchain. This is how/why it works and has been adopted the world over.
Personally, I would say that the whole point of it was not to store censorship-resistant information, but to provide a store of value independent of the current system of state-controlled and/or -regulated fiat currency. The fact that it is also useful for storing censorship-resistant information is a side-effect of the developer adding that feature to the code.