I've had a supermoto as my main form of transportation for about 30,000 miles. Before that, I had a Ninja 250 and... eh. The KLX was far superior as a daily rider. Potholes, poor road surfaces, fuel economy, fun factor, cheap insurance, easy maintenance... The KLX wins on all points.
The only reason I got a second bike (the ER-6n) was because I needed something bigger for long distance travel. America is a freakin' big country and we have a lot of interstates (4+ lane, divided, limited-access, 65mph+ roads). Just to get to Chicago, that's a hair under 600 miles... each way. I've done it on the KLX a few times, but it took me 3 days and I was beat up and didn't even want to hear the word "motorcycle" by the time I got there. On the ER-6n, I make it in roughly 9 hours, allowing for a good lunch break in Des Moines.
Supermotos are very agile, very light, take abuse well, filter easily, allow you to take a shortcut or a parking space that would be a bit tricky with a street bike (and sometimes impossible on a street bike without risking damage to the machine or you), sit you up high and allow you a great line of sight, eat potholes for breakfast, and turn the urban environment itself into your potential playground-- no need to go hunting for twisties when you want to "really enjoy" your machine.
I still prefer my KLX over my ER-6n. I giggle every single time I ride it. I act like a kid on it. The ER-6n is faster, sure, but... eh. It's just not a motard. Plus, I keep getting speeding tickets on it, and it's big and heavy compared to the KLX. It's much less fun in heavier traffic, and you DEFINITELY feel every pothole and bump in the road. I don't even bother swerving around potholes on the KLX that I know would damage the wheels on the 650.
Can't find a place to park? Lean it up against a tree. Bored? Do a wheelie, or take it offroad. In skilled hands, it actually does remarkably well offroad. I am not a good example of this. The point is that you CAN take it offroad into places you would surely get stuck on the street bike and break things.
And, finally, to sum it all up, I will rephrase Bikermole:
You'll have the same fuel range, discomfort, height, and agility of a dirt bike, with all of the on road abilities of a sportbike. It's being able to ride a motocross bike like a motocross bike... on the asphalt. Same flickability, but with street traction. Between a dirt bike and a sportbike, it is the best of both worlds for street riding, especially in an urban environment which has obstacles a sportbike isn't designed to face.