It isn't just distance; Antarctica is surrounded by the harshest seas on planet Earth. The latitudes above Antarctica (aka, the Southern Ocean) are sometimes called the Roaring Forties, the Furious Fifties, and the Shrieking Sixties because of their unrelenting wind storms and furious waves. The wind down there is truly magnificent and terrifying.

Additionally, simple proximity to other land doesnt make a region able to be settled. Yes, tehcnically, Antarctica is "close" to other land, like Patagonia, South Africa, and New Zealand, but these areas are rocky, comparatively barren, and did not practice agriculture until the 19th Century. It isnt the same as being located next to Western Europe, like Greenland.

It should also be noted that conditions in Anarctica are often considerably worse than any of the places you mentioned. The Canadian tundra, for example, still has a discernable springtime filled with game animals. The Deserts you mentioned all have oasises that permit human settlement. And as harsh as the climates of those areas are, they all pale to the unrelented cold of Antarctica. This is important because it isn't easy to make settlements in places like the Sahara or the Canadian tundra. These places represent the upward limit of where humans can settle without seriously advanced technology.

In short, not only is Antarctica the most inhospitable place on Earth, it is also the most inaccessible.

First of all, Antarctica is much more inhospitable than those other areas that you cited.

Antarctica is more often analyzed from an economic and geopolitical point of view. However, we can take a historical perspective. Antarctica was explored primarily for economic purposes; people did want to make money and settle there. Yet economic activity on that continent today is very limited, mostly fishing and tourism. There is a lack of resources that any nation has found worthy of exploitation and transport off of the continent. (“With no native population, Antarctica is far from labor markets and from the markets to which any minerals would need to be transported for final consumption.”) The climate and hostile geography is a huge impediment; there are extreme katabbatic winds that blow throughout the continent and 98% of its surface is covered by ice. As the planet warms, things may change, of course...

An aspect of Antarctica’s history that you should consider is the extensive overfishing of its waters. Governments eventually stepped and enforced curbs on Antarctic fishing, diminishing economic activity in the area.

While Antarctica probably could have supported a native population, it just didn’t; it’s a bit of moot point to ask why when there are examples of perfectly habitable islands that were never permanently inhabited prior to European exploration (e.g. Azores, São Tomé).

See “Antarctica: The Battle for the Seventh Continent” by Doaa Abdel-Motaal, an economist working for the Rockefeller Foundation.

Finally, a question I can answer with my extensive knowledge of Antarctica!

So first thing's first, it is entirely possible that some ancient humans made it to Antarctica (or the landmass that would become Antarctica) but any evidence that proves their existence is undiscovered as of right now. We know that once upon a time ~260 million years ago there was a forest on Antarctica so there was almost certainly more diverse life there than what is seen now. However, much like the forest that was once there, any human or early human life that did exist on the continent either died off or moved elsewhere; perhaps the indigenous people of the pacific islands could even be descendants of Antarctic humans.

As far as Antarctica not being colonized in recent history, the continent itself was not sighted until 1820, well after the initial imperialist surge from the western European nations. It was speculated to exist for almost 300 years prior to its discovery but die to the treacherous waters and out-of-the-way location from the rest of the modern world, no one cared to search for it for a long time.

Moving into more modern times, all nations of the world are forbidden to use Antarctica for anything other scientific research as per the guideline set in the Antarctic Treaty. That and the fact that a majority of the countries on Earth have no property claims on the continent. Come the year 2041 that could all change when the treaty is open to amendments once again. We could see a more commercial or residential colonization of Antarctica in the future, one estimate I read a few years ago was that Antarctica could have a similar climate to northern Canada by the year 2100. This seems like a wild exaggeration of climate change but I suppose anything is possible as technology develops.

If you want to explore a what-if scenario then I would suggest this video here: What if Antarctica Was A Green Continent, the guy who made it does a very good job of exploring the what ifs while remaining within the boundaries of reality. Excluding a few key factors he had to account for of course.

I hope this helps to answer your questions even a little bit! If you have any other questions or need some clarification on a point I made feel free to ask!