Yes fair point. I just checked the highlights for the Arsenal cup game in January and there is just a couple of rows of seats between fans.
I guess the larger area in the video you have provided is to prevent cross contamination.
The sterile area looks unnecessarily big for us, especially with less violence at football these days, I'm not sure I see such a big area at other grounds on the TV. Does anyone know if it's something we do voluntarily or is it set by the FA/police etc?