I've also been cut off once by a car who didn't see me while I was going very fast, but while I braked, I also made a flat turn into the street the car was turning into, and that saved my from a collision.
The rear brake is much more likely to cause a fall. When you apply the brake the bike tips forward and the rear wheel rises up. It easily looses grip and can lock up. That causes a skid and next thing you are on the ground. Or just smashed into whatever you are trying to avoid.
The front brake does not do this because the tipping forward pushes the front wheel into the ground. You get more grip and more braking potential. With a little practice you can stop the bike quickly and easily. You will never go back. But you have to grip the handlebars and tense your arms a bit to deal with the force.
Might also not be an issue for e-bikes, as those are generally heavier and probably less likely to raise the rear wheel while braking.
I'm less than 60kg, and can start to flip a bike if I try.
Ideally, for an emergency brake you want to use 70% front brake, 30% rear brake, get off the saddle and move your bum as far back as possible.
Safe riding everyone.
Shifting weight might help a bit, but you still need to grip.