It doesn't mostly help Tundra/Desert tiles, though. This building is as strong or weaker in Tundra/Desert than elsewhere, because the player wants to place improvements anywhere but Tundra and Desert, and Villages/Towns are no exception.
I reject that premise, as Tundra and Floodplains cities, especially if the former has Stars and Sky or Hunt as the pantheon, can be very food heavy and in need of non-food tiles. Additionally, as bare Tundra/Desert farms are usually either impossible or really weak, villages are the most common way to use those tiles. Thus, I often find myself and the ai building more villages in Desert/Tundra cities, and prioritizing their construction as they can be a huge help for unhappiness. Additionally, the only tiles I would ever build a village not along a road would be in a Desert or Tundra city.
Additionally, the comparative advantage of +1/+1 on a bare desert/tundra village is greater than for a plains/grassland/hills village, and because bare plains and grassland tiles can also be turned into farms. Thus, desert/tundra villages aren't just competing against grassland/plains villages, but against farms. Additionally, Tundra and floodplains cities are usually shorter on gold than Grassland/Plains cities (unless the former has like Furs or Dyes), as they don't have Bison, Cattle, Horses, Sheep, or lumber mill triangles (because Tundra forest is usually full of deer), meaning that you're more likely to be working villages in Tundra and Desert cities to solve poverty unhappiness.
Even if you disagree with my argument that villages and towns are both more common and more helpful on desert and tundra tiles, I don't think a convincing argument can be made that this version of the building would be
weaker in Tundra or Desert cities.