Take my brother and his wife. She originally had a Fiesta, he a BMW 1 series. As kids arrived he bought a Kuga (to carry the crap kids come with). Bear in mind both cars are probably as safe as each other (the Focus being quite a lot newer) - SIL takes the 'big' car to ferry the kids.
To be honest most SUV's aren't much bigger than a standard car, just taller, and research is going into pedestrian safety. They aren't really any heavier. We have a Qashqai, top of the range, so full of stuff, but it was lighter and shorter than my Nissan saloon car.
SUV's is branded about too much - a lot are quite reasonable in size but some of the big stuff - Range Rovers, new Chinese China Rovers, are as big as my van. People do see bigger is 'safer' for them.
My wife did find she wasn't getting people bully her any more after switching from a Yaris.