This may be easily countered by making the mortar round rotate faster. At list that has been the concern in the past. I guess that the laser has to heat the mortal shell so it exploded in mid ear. If the shell rotate slow it may be possible to heat a single area, but if it was to rotate fast you would need much more energy.
Such a system will probably not help Seoul much in an all-out war. According to this article [0][1] N.Korean may have as much as 13,000 artillery pieces positioned along that border, capable of delivering 10,000 rounds a minute. Any anti artillery system will be overwhelmed by thus numbers.
Not if you have 10,000 anti-artillery 100KW laser on vehicles. Let's say each one costs 1 million dollars, you would have to spend 10 billion dollars. Lets' say your operating costs are 3 billion a year (2 man crew at total cost of $100,000 each and another $100,000 for support, maintenance, and command, per unit). Over ten years the system would then cost 40 billion dollars, ($10B upfront + $3B/year x 10 years). This averages out to 4 billion a year. Per wikipedia, there are 25 million people in Seoul metropolitan area. This turns out to be $160/per person per year (or 43 cents per day per person).
You can bet the US government and the South Korean government are going to look seriously at that option.
Let's say my numbers are off by a factor of ten, and each unit costs $10M, and the support is $3M, and the total cost is $40B/year over 10 years: that's still completely worth it, at $1600 per person per year, especially if Korea pays $20B and the US pays the other $20B.
I imagine any rotational speed beyond a certain point is indistinguishable from other, higher rotational speeds in that you are basically heating the whole shell. I don't know how fast these shells rotate, but it seems like it would be hast enough that they are probably heating the whole shell anyway.
Additionally, if you are firing from close to the intended target, you may not have to deal with rotation at all.
Counter Rocket, Artillery, and Mortar (C-RAM) systems have been around for a while using guns rather than lasers - often based on CIWS from naval ships:
