Your average person is not mechanically inclined enough to assess the safety of vehicles, usually to the detriment of the safety of everybody else on the road. Another example of this is people's perception that they're safer with AWD in snowy conditions when all it's doing is getting the vehicle moving faster and giving the driver the confidence to push it way beyond its ability to brake in those conditions.
The most dangerous, a head on collision, will always be safer for the heavier vehicle. It's simple physics.
More than anything, you need to just not be in the accident in the first place. Buying a vehicle with dogshit braking and handling characteristics so you can "win" in a crash you could have just avoided is dumb, especially when you consider that you carry that increased rollover tendency every single second you're driving that vehicle.
Not really sure how you can avoid someone drifting over the line at you...
There are multiple times where I've had to drive on the shoulder to avoid people out of their lane and they would have been a hell of a lot scarier than they were if I had to do it in an SUV/truck. I've been in multiple fairly severe vehicle accidents and I can tell you from first-hand experience that you're not appreciably safer in an SUV.
If you've ever sat in traffic driving a small car surrounded by large vehicles it definitely starts to sink in that you are at a distinct disadvantage if anything goes wrong. So this trend is also at least partially about this weird arms race of wanting to feel safer in the presence of ever larger vehicles.