Why is air travel between South American countries so expensive?

As so often with 'why' questions about prices, it is what the people are preparing to pay and what the companies can offer their services for.

Part of the equation will be the taxes.
Part lack of competition.
And likely there will be no cheaper alternatives by other transport that are enough competition for the airlines to lower their prices.

In Europe, there are many ways to get from one country to an other, including (and not restricted to) bus/coach, train and privately owned car. The distances are such that people will often elect to fly to gain a few hours, but they have the alternatives and many people will use those.
In North America the distances are greater already but still giving other options.

In South America, the distances are often much larger and people are less inclined to travel in the first place, when they have to travel they have fewer options and have to go with what is available for the prices asked.
When you compare the prices to the incomes of the average worker in the countries involved you get an even higher price than in Europe and North America.
If the only option to visit a relative in an other country will cost you a months wages, you do not travel there unless you have to be there.
Rich people will be able to afford to travel, but they can also afford the current prices and often more.

As such the development of cheap travel is much slower, even when there are enough (foreign) visitors to fill the available flights.

My guess is that you have a mix of two problems: the airline you choose and the prices policy. For me, as a Chilean, a round trip from Santiago (Chile) to Montevideo (Uruguay) cost around USD 130, tax included. Try to use a VPN service, the browser in guest/private mode, and get a quote from a low cost

Looking at it the other way around, these are excellent prices and the ones you mention for Asia are insanely cheap!

The main guess would be density of population. We have the same issue within Canada flying from one province to the other. It is extremely expensive and frustrating that domestic flights can cost a significant amount more than international ones elsewhere.

Comparatively Asia and Europe are much denser than South America. This actually compounds the problem because it means there is less business for airlines to compete for and so there ends up being a lot fewer airlines and competition.

As quite usual, flight costs tend to dominate travel costs, so the longer you stay at each destination, the more affordable it will be. Although I was surprised to find out how expensive Brazil is compared to other South American countries and there, the cost of flying was relatively minor compared to staying and eating.

I´m from Argentina and currently living in Netherland. I do like to travel as much as i can. Sadly travel in South America is not cheap, there are a lot of factors..... The "parking" for the Planes is NOT cheap, so usually Airlines pay higher fees to land in different south american countries than they do in Europe or in the US. Nonetheless, what you may lose in tickets you are going to save in food, hotels, etc....

Have you looked at two-way flights? There may be cases where two-way flights are several times cheaper than one-way. Some agents know this, they will sell you a two-way flight even if you're just buying one leg.

Also, some European airlines can offer one-way flights for a fraction of price because they have routes with stopover, and everybody they pick up at stopover is free money for them. Flew this way from Buenos Aires to Santiago with KLM - was the most economical option at $150.