Take a look at this , although this guy made several fundamental errors before he ended up on the ground . If you ever needed to reaffirm your belief in needing to be able to fight from the ground this will do it .
It is a gang assault at one of our train stations in Melbourne by a Sudanese gang on a small guy , I mention their race only because if you have ever seen Sudanese they are freakishly tall , anyway we have a bit of a youth gang problem with some of them in our cities.
They followed this guy and punched him to the ground and gave him a kicking so hard his head was bouncing off the wall . Using some of the techniques from your video this guy would at least of been able to take down one or two of the attackers while he was on the ground or at least get so close to them to deny them any space to generate a powerful kick .
Probably would have been a good idea for him to get his arms up to shield his head against the kicks , or at least take most of the sting out of them. I have done a bit of experimentation in deflecting various types of kicks from a sitting position on the floor and I found that the most effective defence is what we call Seung Bong a two handed deflection with one forearm on top of the other.
Because of the inability to pivot you will still tend to take a lot of force on the arms . But you can still manage to turn a little bit with the upper body and as long as the deflection is moving on contact with the leg then you can spread the force a little over both forearms and take a fair bit of the force out of the kick , your arms might get broken if you don't time it properly but its got to be better than being kicked in the face.
From this position if you are quick enough you can even capture the leg and do a take down from there.
Have you done much work against stopping kicks from the floor in your school and if so what did you think were the most effective techniques ?