Btukfyl

In film, images are typically shown to us at around 24 frames per second, but modern sound files will often have 44100 or 48000 samples per second.
There's a threshold above ~12 fps where we will perceive successive frames as unified motion instead of individual pictures (c.f. phi phenomenon, persistence of vision, beta movement). But to get this unified experience in the auditory domain, we need a much higher "framerate". Why is this?

Sound is pressure waves; young humans can hear (aka, detect pressure waves) up to about 20 kHz. To produce these high frequency waves with a speaker with a time-domain signal, it is necessary to have a sampling rate at least 2x the highest frequency that will be represented. In practice, those very high frequencies aren't included in music, and definitely aren't included in speech, so ~44kHz is sufficient. There is a membrane inside the cochlea that is structured to vibrate at different frequencies along its length. At the higher frequencies, neurons don't actually respond to every sound wave, they respond to the envelope, so it is possible to respond to frequencies much higher than the frequencies that neurons can even fire at.

Vision depends on detection of photons. A photon hits a photosensitive molecule in a photoreceptor in the retina, which causes a chemical change. That changed chemical binds to a protein, which causes a cascade of events that ultimately causes a change in the release of a neurotransmitter. Vision is slow: the cascade in response to a single photon takes on the order of 100s of milliseconds. We can detect things a bit faster than that because the visual system responds to changes so the slope of that response is a relevant feature, but overall this slow process means that light information is low-pass filtered. As long as a signal is sufficiently faster than this low-pass filter, differences between a frame-by-frame versus a smooth signal are mostly not noticed. However, it isn't true that 24 frames per second is a limit. Modern monitors often operate much faster, such as 60-144Hz, because these faster frame rates are important for perception of smooth motion at high speeds. Slower frame rates are sufficient when changes are small, however.

In nature, a lot of things vibrate a high frequencies into the 1000s of Hz, so there are good evolutionary reasons to detect high frequency sounds. However, very few things move at those speeds, and those that do are typically not behaviorally relevant (e.g., you don't need to see every sweep of an insect's wings to detect it as an insect).

I don't have a full answer, but it might get things started...

You are mixing up two concepts frame rate and sampling rate. In a video presented at 24 fps each frame, potentially, has a wide range of spatial frequencies. Typically the spatial frequencies are limited by the number of pixels, but you can low pass filter each frame to reduce the spatial frequencies (you will end up with a blurry picture). This spatial filtering has nothing to do with frame rate.

The 44.1 kHz sampling rate in audio signals is more akin to the spatial frequencies of a picture/frame than the frame rate of a video. An example of audio frames would be something like decomposing the audio signal into a bunch of slices with the short time Fourier transform (STFT), setting each slice to have a constant spectrum (and phase???), and reconstructing. Reconstructing the signal from a modified STFT is non-trivial (cf., Griffin and Lim 1984). Given the difficulties in the process and the lack of an application, I am not sure anyone has really investigated how the duration of the slices affects things.