Nothing "requires" anything, although when the bars get low, rear-sets tend to be the best ergonomically for many riders.
Would depend on your specific machine, your own size/proportions, and the desired riding position. I'd guess that for most riders on most bikes in most situations, drag bars are about as low as you could/should go before rear sets become the most reasonable option. But your mileage may vary.
At least it is an inexpensive thing to try out if your bike already has tubular bar clamps. Coupla minutes swapping everything out to a super-cheap Emgo bar or something and you'll know for sure.