It basically comes down to the fact that affordable and portable cameras can't deliver top speed and top quality at the same time. The problem is not the sensor.
Firstly mechanical shutter gives better results than electronic but the mechanical shutter on cameras while fast is not designed to run continuously at high framerates. A high end DSLR might have a rated shutter life of 300000 cycles which sounds like a lot, but at 60FPS it translates to only about 1.4 hours.
Secondly and more importantly the data just becomes unmanagable. Lets say you have 20 megapixels and assume 12 bits per pixel raw. That works out to about 1.8 gigabytes per second at 60fps. Storing that kind of data gets into the world of big raid arrays.
It would be possible to build a camera that could capture 20 megapixels raw at 60fps and with a mechanical shutter system designed to survive such use but such a camera would be extremely bulky, heavy and expensive.
So DSLR vendors offer seperate "video" and "burst" modes with different tradeoffs.
"video" modes are designed to offer sustained high framerates but at a heavy price in image quality. Electronic shutter is used, the image is typically rendered from raw to RGB or YUV, then cropped or downscaled, then heavy compression is applied. This reduces the data rate to something managable for storing on a fast SD card.
"burst" modes can give full quality but the framerate is lower and there is a limited length of burst before the photographer must stop and wait for the camera to write out the collected data.