Why would a zoom suffer less from diffraction?
It's an interesting observation that zooms can be stopped down a little more than primes. Mathematically, given the same f stop, the size of the blur pattern of a point source caused by diffraction should be the same, so the degree of 'softness' should also be the same. There might be some variation caused by different aperture shapes, in that a polygon will create spikier blur patterns than a circle, but I'm not sure that zooms are any more or less prone to having polygonal apertures.
One small factor could be that cine lenses are commonly marked in T stops, and since zooms will usually lose more light than a prime, the same T stop in a zoom will be a smaller f number in a prime. In other words, a zoom needs to be stopped down a little more in terms of T stops to reach the same f stop as a prime. But with modern lenses we're probably only talking half a stop difference at the most.
I think David's observation that sharpness is often subjectively appraised is the main explanation. Apart from the sorts of shots a zoom might be used used for (like the close up of a face as mentioned), the improvements gained by stopping down a zoom probably shift the sweet spot balance further towards a smaller aperture, outweighing the softening effects of diffraction.
At what aperture do you find diffraction start to become noticeable, in motion picture?
Like pin-pointing an exact depth of field, nominating an aperture where diffraction starts to be noticed is somewhat arbitrary. When is sharp no longer sharp? How good is your eyesight? We can determine mathematically the size of an Airy disc (the interference pattern of a point source caused by diffraction) directly from an f number:
diameter of airy disc = 0.000045 x (f number) in inches (from Arthur Cox, "Photographic Optics")
At least this is for green light - a mid spectrum wavelength. Blue light will create a smaller disc, red light a larger one.
So in simple terms at f/11 any lens will turn a point source into a blur circle of around 0.0005" in diameter.
We now need to decide if a 0.0005" diameter blur is an acceptably sharp rendering of a point source. Traditionally, to determine DOF tables, lens manufacturers and cinematographers have relied on a defined maximum allowable blur circle diameter that could still be considered sharp - a Circle of Confusion figure. These figures may vary wildly depending on factors like the format size, the final viewing size and distance, and these days also the size of the camera sensor pixels. But typically, 35mm movie lenses have used a CoC of 0.001" (0.025mm) and 16mm lenses a CoC of 0.0006" (0.015mm).
So looking at those figures, the blur circle at f/11 is nearly as large as the historically accepted Circle of Confusion for 16mm format. By contrast, the historical 35mm CoC figure is not reached until about f/22. Many people might argue that the modern CoC value for 35mm format should be tightened to 0.00075" (0.019mm), which places the acceptable diffraction boundary at about f/16. Some even argue for 0.0005", which means f/11.
With digital cameras, the pixel size gives us a physical limit to the effects of diffraction. Alexas, for example, have photosites that are 0.00825mm wide, which after de-bayering and downscaling effectively become 0.0124mm wide. So diffraction has no discernable impact on Alexa's resolution until around f/11, where the blur circle begins to fill a pixel. But just how noticeable the softening would be at f/16 depends on lots of variables.