Clearly you don’t operate in 3rd World big city traffic. That’s where the 3 second scan makes sense.
On a US interstate out in ruralia? Your method works fine.
My niece returned from a trip to Manila astounded at the traffic.
I’ve periodically wondered, if I am approaching a cross street with 1 lane of traffic in either direction, and traffic is flowing in both directions with maybe 5-6 carlengths between cars, how much of the street is “solid” vs empty? Probably too many variable to calculate. But if you drove a car into the intersection into moving traffic - say every 10 seconds (magically removing any wreckage between each “test”) what percentage ofe of cars would cross without accident?
Sort of another scenario - what are the chances of an accident if you just blow through a stop sign. Sure, it can never be considered “safe.” But depending on the amount of cross traffic, the odds of a crash might be pretty low.
This i would equate to the question “To get the least wet, is it better to run or walk in the rain?”
Instead of thinking of traffic or rain fall as a moving stream, imagine it at a standstill - so many raindrops per cubic meter not moving, or 1,2,3 lanes with an X% chance it contains a car in a specific point.
So now, instead of going straight across the road, consider the area you sweep out while moving through this rain or crossing this road. The volume you sweep out will be an angle of the cross-section you present, for the amount of time you are present. Logic obviously says the faster you cross the road (and at 90°) the less likely you are hit. (Of course, the faster you run for the rain question, the greater the angle you present to the rain, it hits the front as well as the top)
If someone only built a test machine for you
As soon as I read your post, I KNEW what you were gonna link to! 
Works like any running red light, when you can see what’s coming with decent warning, and stop on a dime (or log).