The answers and comments so far provide very thorough insight about why concepts in crypto are hard to prove or analyze. However, I think there is still room for tackling another side of your question. Beyond the specific challenge of proving the information theoretical security of a primitive, your question is why does crypto fail?
In my experience, there is a huge gap between theory and practice in information security, and particularly when cryptography gets involved. Sure, there are libraries and products designed thoroughly, with the best intentions and the best knowledge, but the fact remains that bad crypto is implemented around critical systems all the time (to see how bad it can get, http://www.cryptofails.com/ has some terrible cases documented). I have seen people dubbing Base64 encoding as "64 bit encryption", and just some minutes ago a question here asked for a broad comparison between AES and HMAC (whereas they are not equivalent primitives in any sense).
And that's not their fault, as they are likely skilled developers, but an indicator that cryptography has a huge learning curve to be used properly (even if supported by "flawless" implementations of the primitives) and has a lot of nuances that can lead to a buggy implementation (if you see the code that lead to Apple's goto fail, the culprit is a single and apparently harmless line of code).
So, to summarize my main point, information theoretical security proofs are an essential starting point, but a lot can go wrong from there.
As for the "but the assumptions are obvious or definitional", you might want to take a look to the paradigm shift that would be implied by quantum computing. Factoring the product of large primes is hard now, and probably will be then, in the sense that it won't suddenly become trivial, but it might not be hard enough to be used as the base for cryptographic operations. The assumptions are good because they have held so far, and are likely to hold given the status quo, but might not hold at some point, and then the proof crumbles.