Or has Dumbledore found it so useful to carry a large rock around that "get a big rock, keep it with you at all times" is in the top five things he'd tell his younger self if he ever got the chance? Seriously -- the fuck?

The obvious interpretation of this is that spellcasting is a skill like any other, and practice develops it. By giving Harry an implausibly large object to carry, and then having him interact with the Transfiguration professor, Dumbledore can be fairly confident that Harry will try to transfigure the rock into something more reasonable to have in constant physical contact with him. This constant transfiguration practice will help Harry level up his abilities, and a huge rock is predictably useful in combat situations.

Here's a short list of rules violations:

He also showed off his unique partial transfiguration trick during combat, which Dumbledore was hoping he would save for the Final Battle.