Can someone explain what the advantage of this is over a typical optical visible range satellite.
As an indication of how sensitive it is, you can use SAR interferometry to see where Crossrail tunnels have been bored under London, despite the elevation change of the buildings and roads on top being too small to have had any impact on their structural integrity. The caveat is that this level of sensitivity you get when looking at smooth, undisturbed surfaces like the roofs of buildings isn't matched when you're looking at fields with growth and soil movement
a flat roof (with fine enough texture) will be reflective thus invisible. What you see are precisely tiny "corner" reflectors formed by large enough gravel, rocks and building structures. On a mountainous area, as long as you have some rocks and gravel here and there, you are still able to find correlations--and thus interferences. Of course, if all you have is wet mud and vegetation there's nothing to do, but this is not often the case. In a region of special interest like near a mine, people often install ad-hoc corner reflectors at calibrated positions.
It’s not a replacement for visual range (or infrared for that matter) but an additional sensor. It’s usually used to create things like elevation maps. So all those altitude measurements that you see on Google Earth might be at least partially SAR.
Perhaps you missed the point of the article?
While it is true that some implementations of SAR can image through walls at short distances (tens of meters), SAR is a very broad term and those systems are very different from the imaging systems in the article.