In this story, the narrator has traveled thousands of years into the future. This might be a utopia for a tired man or for a man who prefers uniformity/conformity to any type of conflict or struggle. But for the narrator, and perhaps the reader, this is a dystopia: a dreary future. Thus the tone is foreboding, a warning about a possible future which has lost virtually all subjective human qualities.
While it is nice that poverty is a thing of the past, and that people live as long as they want to, this future lacks diversity and also lacks any sense of history or progress. It seems that future humans have sacrificed emotion for stone cold logic. The man from the future says that people of his time try to live "sub specie aeternitatis" and this means to live under the aspect of eternity. (This is from Baruch Spinoza, but has been commented upon by other thinkers, philosophers, etc.)
To live under the aspect of eternity is to live outside of time and outside of history. In terms of art, this could mean to call an artwork "timeless." But, in this story, in such a world, there are interests in present, past, or future; so nothing is timeless in the sense that it is known to have been appreciated in successive eras. There is no context about a particular era: all times are considered to be an amalgamated "oneness." This future is a world of forgetting. The man from the future indicates that this leads to a more peaceful society. But this is clearly a directionless, boring society. With no concern for the notion of memory, historical progress, or diversity (among people and eras), this world seems quite barren. And with no concern for history, this society has credited Hitler as a philanthropist. He says it is a world of forgetting the past, but clearly they have mis-remembered Hitler at least, and probably have mis-remembered other things. It is a clearly flawed future (some pros, more cons); the tone is therefore drab, gloomy.
But Borges, typically raising more questions than answers, ends the story with a poetic line that even sounds hopeful:
In my study on Calle México still hangs the canvas that someone will paint, thousands of years from now, with substances that are now scattered across the planet.
It is a pleasant thought that substances scattered across the world will be united in this painting, sometime in the future, and then given as a gift. But fit this notion with the concept of that uniform, boring future. In the narrator's time, the substances are scattered, diversified over the world. In the future, they are consolidated, squeezed into one thing, for one purpose. The diversity is gone. So, a pleasant thought, put into context with the drab future, is actually foreboding. Note that the other canvases are nearly blank. A world of no nations, no private possessions, no subjectivity (everyone is anonymous, referred to as "you"); there is no noticeable difference between you and her, this and that. The future world is like those canvases: lacking detail, diversity, nearly blank.