I'm from country without nuclear weapons and even I think that idea is really bad.

Here's why, either Russia or China could launch a first strike if they believed USA wouldn't retaliate. Or simpler they would use conventional means more aggressively and if that escalated to conflict with USA then they would simply make first strike. Key point is neither country should ever think USA would definitely NOT use nuclear retaliation on nuclear first strike. In a sense by making a major nuclear weapons power less likely to do use its own weapons increase overall chance of nuclear war. And finally this system also gives additional urgency for aggressive actions for opposing great powers, by forcing them to act and finish all their aggressive plans during term of a president they perceive in capable of ultimate action.