You miss one thing, though: the block chain has real costs. If you want another block chain for the document timestamping, for instance, then you'll have to convince people to mine that block chain. Inevitably, it'll be just another currency not very different from Bitcoin. And since both have almost the same objective properties and Bitcoin is already more valuable, nobody will spend CPU on your currency. So you'll end up using the Bitcoin block chain anyway.
This is exactly what is happening to Namecoin: initially, it was just another blockchain, but very soon people realized that nobody is willing to spend any CPU/GPU time on Namecoin if Bitcoin is worth more (no matter how much more). So Namecoin guys proposed "merged mining", which is just a fancy way to reuse proof-of-work done on Bitcoin block chain without asking people to devote any resources specifically to Namecoin.
This is exactly what is happening to Namecoin: initially, it was just another blockchain, but very soon people realized that nobody is willing to spend any CPU/GPU time on Namecoin if Bitcoin is worth more (no matter how much more). So Namecoin guys proposed "merged mining", which is just a fancy way to reuse proof-of-work done on Bitcoin block chain without asking people to devote any resources specifically to Namecoin.