Why does this require "hard" braking? If another car cuts in front of you just decelerate gently. You don't brake and wait until the gap is big enough (also if this is stop-and-go traffic, you should be trying to avoid braking at all)
Indeed, when someone changes lanes in front of me, I gently let off the accelerator, but as someone else noticed, that can enrage drivers behind me (I don't take it personally), and I'm definitely traveling fast enough to remain in the middle lanes.