In just under 2 Million miles of driving ND, SD, MT, MN, WY, NE, and IA, since I started traveling for work, I've hit 1 deer, and none before that either having received my driver's license in 1989. I hit that deer maybe 5-10min after sunrise, on Hwy 2, driving west, with the rising sun @ my back, on the way to MT to go deer hunting. Headlights wouldn't have mattered at all. They've mattered a whole bunch of other times, but, given that I've never hit a deer in the dark and I drive exponentially more miles than the vast majority of folks, my take is that most folks aren't overdriving their headlights. Most people are overdriving their attention span/alertness/situational awareness. I've also gotten 1 big raccoon in the middle of the night. Beyond that, all of my car/animal incidents have been birds during the day. Never a coyote, stray dog, cat, rabbit, badger, or skunk, day or night. I've braked-for, avoided, and or dodged Moose, elk, wolves (MT and MN), horses, and cows. No accidents at all with other vehicles, ever.
I've logged hundreds of thousands of miles through very thick "deer country" when ND/SD/MT were one giant ocean of CRP and managed to keep the deer off my vehicle, whatever vehicle that's been. A miss-mash of work and personal vehicles. Cars, mini-vans, SUV's, and pickups, 9 manufacturers I can think of off the top of my head. Older dimmer headlights, and fancy new LED's. It's not the lights.
Focus on the task at hand, keep your eyes where they need to be, on the road and scanning ditches.
It's not a light brightness problem, and it's not a speed problem, and it's not the 2 coupled together, unless the driver has an attention/awareness problem.
