Why do cameras in 30FPS mode operate with faster Auto focus than in 24FPS?

[Truthler]

Hello!
What is the physical/technological reason behind this phenomenon?

Why do cameras in 30FPS mode operate with faster auto focus than in 24P mode? It is true for Canon, Sony Panasonic JVC ...
Sometimes the picture also looks cleaner, despite the 30FPS is more demonading on the same bitrate than the 24FPS.

[filmboss80]

When using the automatic settings in your camera, the manufacturers change various default settings whenever you change the frame rate. These includes the shutter speed (the amount of time the shutter is open) and the aperture (also known as iris, measured in terms of f-stops, which, in auto mode, opens up or closes down based on the amount of light passing through the shutter). When all these things change, it affects the depth of field; that is, the range of distance in which things stay in focus. If you have a long depth of field, the auto focus takes less time finding its focal "sweet spot." A shorter depth of field gives you a more limited focal range; thus the auto focus has to shift a lot to find that very narrow sweet spot.

[Truthler]

When using the automatic settings in your camera, the manufacturers change various default settings whenever you change the frame rate. These includes the shutter speed (the amount of time the shutter is open) and the aperture (also known as iris, measured in terms of f-stops, which, in auto mode, opens up or closes down based on the amount of light passing through the shutter). When all these things change, it affects the depth of field; that is, the range of distance in which things stay in focus. If you have a long depth of field, the auto focus takes less time finding its focal "sweet spot." A shorter depth of field gives you a more limited focal range; thus the auto focus has to shift a lot to find that very narrow sweet spot.

So can it cause that I generally see a more focused and cleaner image in 30FPS, despite the bitrate is the same? It also shows little less video grain (maybe this related to the more stress on bitrate) ?