The pushback speed cannot be changed, because it's obviously linked to the walking speed of the wingwalker so, if we just made the pushback truck faster, the wingwalker would remain behind, so you would still have to wait for it, which is the same as if the pushback was like it is now.
The reason why the wingwalker should say close to the pushback truck, it's because they must keep the headphones cable plugged in to talk with the pilot.
If we accelerated the wingwalker to keep up with a faster pushback truck, it would look like funny and wrong, like the silent movies from the 10-20s
The pushback video you show was made with a Towbarless truck and there was no wingwalker, so I guess they could go faster and probably had a direct audio connection with the cockpit. The video looks a bit accelerated also, because the caution lights on the pushback truck seems to pulse a bit too fast.