One very nature rationale is that in R^2 we have two standard bases. For a square grid, we only need to change the value along one base to get to the nearby point.
screens in reality are squares, so if pixels are also squares, you don't need to deal with edges
another reason I can think of is it helps build an easier coordinate system. if everything is a square, we can locate every square's exact location easily by knowing it's lower-left corner, while triangles or hexagons are more complicated.
Are there any grids in which the pixels don't line up, like if we tried to use circles instead?
Could it be due to the reason that square grid makes it easier to express points in 2D coordinates and calculate the Euclidean distance between points?