When braking hard, not necessarily a panic stop, I apply both brakes until the back tire starts skidding. Then back off the back brake. Never had any problems with the technique. Unless I'm in a turn, the road is wet or some other condition causing problems.

I can only remember having 3 "cartwheels" in my biking life. That's not counting meetings with autos, side slipping in the corner, etc.

The first at 12 yrs, I was riding down a steep bumpy path in a quarry. Too steep. I never touched the brakes. But I hit something! Never knew what.

The second at 19 yrs another quarry, we were using a steep downslope and a small berm to do jumps on our 10spds. The other kids were jumping higher than me! So I pedalled down hard hit the berm and really flew! Mid air the bike rotated forward and we landed in a face down position.

The last time at 20yrs, riding a borrowed bike, the brake lever fell off into the front wheel still hanging by the cable. I was in a hurry so I continued pedalling, leaned way over the front tire, pulling on the cable, cursing all the while. The lever slipped crossways into the spokes. The front tire stopped spinning. I managed to stop the bike by applying my face to the sidewalk.