A frustum is used to clip geometry, deciding which parts of it are visible. It seems that most cameras use a frustum shaped as a pyramid segment, i.e. a box between two rects of equal alignment on parallel planes. If the field of view is small (below 40 degree or so), this produces excellent results.
However, for larger angles, this design has a weird consequence: Objects in the center of the screen are clipped 'earlier' than those at the edges, i.e. when less far from the camera origin. This is caused by the far clipping plane being a plane, not an arc. So the Euclidian distance from camera origin to the frustum corners is larger than the distance to the far clipping plane. If the field if view is larger than about 100 degrees, the distance can in fact be twice as large or more.
As a player, one will quickly learn to look diagonally to see more. I've always found that pretty strange. Given that we mostly focus on and look at things of interest in the center of the screen, this is the exact opposite of what I would consider sensible. The view distance in the center should be at least as high as near the screen edges.
So it would seem more useful to either use an arc or quad instead of triangle to define the clipping area.
Regarding performance, I don't see a problem in making such a change at all. An arc, for instance, would replace the which-side-of-far-clipping-plane test with a squared distance check - pretty much the same. Replacing it with a quad would use the Manhattan distance instead, i.e. the player can see further in the center of the screen by factor sqrt(2).
On the other hand, only rendering stuff that is actually in the visual focus area, a lot of geometry can be excluded: at higher fov, half of it or more! There is also drastically less loading/unloading of objects when they enter and leave the visible space.
I've seen this implemented comparatively in games: The results were clearly superior, allowing larger view distances at the same performance and removing the diagonal-pop-in effect common in many games.
So I'm wondering: Why is the classic pyramid frustum still used everywhere?