Edit: ^^^^ No it doesn't.
SORNing and unSORNing a car is more than a slight inconvinience, for one it means you have to insure your car about a week before you want to actually drive it because you'll need the paperwork to hand before you can get tax since you'll have to do it the old fashioned way, at a post office.
If someone chooses to drive without insurance they'll have no qualms about driving with no tax either so I don't see how it's going to remove all these uninsured cars from the road.
Also, here's a situation that happened to me a few years back. I had the engine go in my Legacy B4, so I had it recovered to a specialist repairer, Scoobyclinic in Chesterfield. I was living in the south east at the time.
It ended up taking 3 months to repair due to difficulties with the warranty company and then needing to obtain a new engine. My insurance only had one month left, so I let it expire, and when I was told the car was ready to collect I took out a new insurance policy and up I went to collect it.
Now under this proposed new scheme I would have had to make a special trip up just to collect the tax disc so that I could SORN the car.
Alternatively I'd have to argue with the court that while it was in the care of Scoobyclinic it was covered by their insurance, which would also be difficult to prove.