The only advantage SUVs offer in safety is that they're likely to flatten the other car in a crash. Aside from size, the characteristics of an SUV make safety worse—they handle badly, tend to roll, and their design is unsafe to pedestrians and cyclists—so buying an SUV makes the roads as a whole less safe. People buy SUVs to avoid being killed by SUVs. It's a negative-sum arms race.
SUVs have atrocious visibility, and this has its cost in blood. They are so high off the ground that it's impossible to see what is near to the vehicle. Thousands of children are injured every year from drivers not seeing them over the hood. Hundreds are killed. This kind of incident has a name: the frontover.
SUVs are a major cause of poor visibility. The need to see over other cars mainly exists because cars are so stupidly tall. Buying an SUV to see over other SUVs is another negative-sum arms race.