How is a 10 minute continuous exposure functionally different from 10 minutes of video with every frame stacked? In the former, each photodiode acts as a compositor for each pixel instead of whatever algorithm is chosen to combine frames in the latter?

You pay the read noise every time you read out the sensor and digitize the values. Also, you lose a tiny bit of time between exposures as the sensor resets itself. And you might have a bottleneck in moving the data off the sensor and saving the image. Furthermore, if you perform lossy compression on the video, then your digitally stacked image will differ significantly from analog stacking on the silicon sensor.