Well in fairness Burroughs generally doesn't mention what anyone is or is not wearing, unless it's a specifically relevant fact (like the waking up naked on Mars). You could as well say that he doesn't mention JC's hair so JC is bald. All we know is that Burroughs doesn't actively negate the possibility of nudity. Textually you could say the same thing about Tarzan except that in his case he meets people and they don't react to nudity. John Carter's original publication pulp magazine covers, the interior bw illustrations, and book wrapper jackets from 1912 through to Frazetta in the 1970s as well as 75 years of comics obviously wouldn't support the nudity either.
While I agree Burroughs didn't linger on dress often, he did describe Tarzan as wearing a loin-cloth. And his descriptions of the Green and Red Martians do specifically mention nudity.
Green Martians: "With the exception of their ornaments all were naked."
JC's description of Dejah Thoris: "She was as destitute of clothes as the green Martians who accompanied her; indeed, save for her highly wrought ornaments she was entirely naked, nor could any apparel have enhanced the beauty of her perfect and symmetrical figure."
Burroughs mentions JC describing the heat of the sun bearing down on his naked skin was fiercely hot, like the Arizona desert. As far as illustrations from the early books through to Frazetta, it would only stand to reason that they would add "clothing" of some sort so they could actually publish the things without running afoul of the prudes that predominated American society for so many decades.
But, that's all moot. However she (or JC) would be made, as long as it was "close" to the original source material (and not that horse-s87t movie) would be fine by me.