If the road is a divided highway and the median is large, I can see it working just fine. In this case, I think the right side was better.
I see a couple of problems with using the grassy median.
1. It is grass/dirt/mud. Traction is reduced, which affects deceleration as well as acceleration after the stop is finished.
2. Grass/dirt/mud is harder to drive on.
3. The median is often slopped away from the road.
4. Fire hazard as seen in the video.
5. Generally, traffic in the lane closest to the median is travelling faster than the right-hand lane. Makes getting back on the highway harder.
6. Many states have laws that require other drivers to slow and/or move over one lane when passing an emergency vehicle. "Fast lane" traffic moving into the "slow lane" is unusual and may cause problems.
7. If the car needs to be towed after the traffic stop, now the heavy tow truck needs to drive on the soft surface of the median.
8. Most states require a driver to move to the right when an emergency vehicle is behind them. The median is not to the right.
9. The grass might hide obstacles that could damage the car or cause loss of control.
The first time I saw someone move to the grassy median when being pulled over was on I-95 in MA. I think I posted about it here. His actions almost caused a multi-car crash, because he pulled onto the median without slowing down first. He damn near lost control of his car. The state trooper that was following him had to move hard to the right to avoid hitting the idiot, which caused many other cars to have to slow or move in reaction. This happened at busy time of day on a four lane portion of the northbound side of I-95. It would have been a big crashy mess.
