Some people prefer the higher up seat position and climb instead of crawling into their cars, but you were right about other things, and according to IIHS, of all the fatal road accidents in the US, 58% were regular cars and 24% were SUV, which doesn't seem so bad at a glance but if you factor in the overwhelming total percentage of regular cars on the road (>15:1) and relatively small number of SUVs, you can say that the SUV is at the very least not a safer option.
And according to some studies, the higher seat position actually contributed to larger and wider blind spots , especially front and back of the car. which may raise the accident rate in cities where pets, small children and low/small obstacles were more common.
One sad accident happened last year in my local area involved a X6 , the driver failed to spot a small kid passing from the rear right side of the car while the driver was trying to reverse down his driveway to his right, the car knocked the kid down and ran him over twice. The driver thought he drove onto the curb .