1) How common of a problem is this for freeskiers? Is this an important issue to address?
Of course this is an important issue. Any time you loose a ski while skiing or landing switch, the brakes are a concern. If you never ski switch, they're fine. However, I happen to enjoy riding around backwards, and a lot of other people do too.
2) Why do you think freeskiers are more prone to breaking ski brakes?
We land and ski backwards. Duh.
3) Stories of broken ski brakes
Too many to count. On a few of my bindings, the brake arms (Salomon) can come undone from the brackets that hold them in. This is the result of these wrecks.
4) Stories of run away skis that created a safety hazard
Many. I had a Caylor fly about 500 ft down a cliffy run at Big Mtn earlier this year.
Designing these wouldn't be that hard. Here's what I'd do.
The fulcrum of the ski brake is the main stress point in a switch landing. It's also the place all the forces of the brake act on the brake frame. If the frame isn't strong enough, the bracket at the fulcrum breaks, and the brake arms fly loose to be only connected with the pedal. If the brackets don't go, it can wrench the whole brake loose, break it, or even damage the binding plate/plastic construction.
The problem is that the brackets at the fulcrum cannot move. When a ski catches going fakie, the forces that the brake arms produce push the fulcrum brackets toward the nose of the ski. What I would create would be a lateral plastic/rubber slot mounted in a thin metal frame for the bracket that goes around the brake arm. It would extend out towards the nose of the ski from the current fulcrum point. At the current fulcrum point, there would be small notches in the slot holding the brake in that place. But if the brake arms catch, they could push past the notches and slide along the track towards the nose. This wouldn't interfere with the any pedal is currently set up. At the end of the slots, there should be some sort of rubber damping system to take the shock of the direction change, and prevent bending the brake arms/damaging the brake as a whole. If the ski changes direction after the initial catch, the arms are pulled back towards the notches, and they work that way too.
I just want someone to make these. If you use my idea, send me a few pairs.
Please remember that any brake arms you use should be bendable. Shelling out for wide brakes to make up for a 5mm difference is stupid. Salomon arms are, in my experience, the easiest to bend.