Most inexpensive shredders have a very low duty cycle, so they'll cut out or overheat if you shred continuously for more than a couple of minutes. That's fine if you shred a couple of documents at a time, but it's infuriating if you have a big box of documents that need to be shredded. Heavy-duty shredders capable of continuous use are bulky and heavy, which is a significant issue if you live in a small apartment.
Domestic burning of household waste is illegal where I live, I would have thought it would be illegal most places in the Western world by now. Burn paper = CO2; shred paper = more paper.