Why do they deliberately (?) crush the quality for any video sent in by "normal people"? Whenever they (TV stations, YouTube channels, etc.) show footage shot by "normal people", even current such, it always looks like they used a cheap consumer video camera from 1981 with a worn-out VHS tape and then processed this on Adobe Premier 1.0 on Windows ME with the lowest possible quality settings and then recorded the screen showing this video with an even worse camera which then was processed further to just become a blur of pixels.

Assuming that what I said is nonsense, how is it technically possible for the quality to be so incredibly bad? Any person with zero artistic or technical skills can, today, just hold up a "smartphone" and video record any event in crisp, clear quality. It's difficult to make it look bad unless it's very dark and you constantly shake the camera around like a madman.

Surely they must be applying some kind of "crusher/uglifier" filter on these videos, to remove details/quality? I can't see any other explanation. But why do they do this? Is it that they can't stand the idea of it being "stolen" and re-used, so they sit on the real quality version and never show/broadcast it as it was shot? But then their own broadcast also looks crappy, so that also doesn't make any sense...

None of this makes any sense to me.
Without an example it's hard to say, but I think perhaps sometimes people just hold up their camera and film, they can't or don't frame the shot or adjust the zoom, they're often standing in one place and can't get closer to line up a good shot. Also lighting is super important for good video, unless it's filmed during the daytime in sunlight, the quality really suffers. 

If the image is cropped and zoomed for television, it will amplify camera shake (and most of these videos are handheld) and reduce the quality a lot.

I also think most people don't have high end phones. Even really good phones suffer terribly in low light. I think it's quite easy to underestimate how poor video looks when you view it back on a phone too - if you export it and view it on an external screen, the lack of quality becomes much more noticable.