During that 30 days every one of those pieces of paper would be a liability for the shredding company - they'd need to be protected against tampering with the same degree of diligence as the client uses, despite 99.999% of them being destined for shredding.

There are also a lot more failure modes for delayed shredding. For instance, what if you asked for a document back and it couldn't be found? Could you be sure it was "shredded by accident" and not stolen? Will your regulators be happy with that answer?