Real minimalists take less than their fair share, not more.Are you defining "fair share" as "median"? or as "takes less than what he produces, as defined by how much value others think he provides in terms of how much money they give him for his work"?
Much as you may dislike capitalism, and whatever flaws it has, it's the best system we have for identifying the value of some product or service: a thing is worth what someone else is willing to give for it. Expanding thereon, note that that thing (product or service) is probably worth _more_ because one can usually turn around and acquire/generate even more wealth with it.
OP writes a blog post. He acquires enough income somehow from it to pay for a seat on a cross-country flight. What he pays for that seat in turn nets not just enough to cover costs, but to turn a profit on that flight. That profit in turn allows employees & shareholders to buy [insert warm fuzzy life-enhancing goods/services here]. During said flight, he writes another post which will net an income enough to cover the next such cycle. Upshot? he buys a red-eye flight instead of paying for a bed (divided by however many nights he would own, but perhaps not use, said bed), "minimalizing" that bit of his life, and the world is better for it.
You may think it's "not fair" somehow, but you're not willing to put up the value-representing money to trump it. What's your "footprint"? and how might that be criticized? (say, by the "strip mining" of forest land for carrot farms.)