Mass panic puts time pressure on negotiations
Q: "My question is why risk a nuke since so far no one is capable of intercepting it anyway? Why not just plot a direct route and let it scram at low altitude until it crashed into the target zone if efficiency is all that matters?"
For some reason, the agressor decided to let the missile fly multiple rounds in the atmosphere.. at Mach-5, that will take about 6-7 hours for a round trip, depending on latitude of the flight path. It could be up there, for a day or two. I'll skip the feasibility analysis and technical frame challenges "it's a waste to do this", other answers have covered that. This is an attempt to improve on Alexander's answer. Why would this weapon be the perfect way, to put pressure?
Extremely low orbit will not allow secrecy to prevent panic
Say 200-500 feet altitude, modern guided missiles can do that. All the time, this frightening nuclear missile will fly over your populated areas, multiple times, visible to everyone in the target areas. It will be in all the newspapers. And feel like Russian roulette (what's in a name)
Uncertainty: no tactical or strategical response, it could even be fake
The defending army would get intimidated - air defense will do 3-4 attempts to intercept the thing.. and no attempt will succeed. That would undermine army moral. Especially at high command levels.. your country is a super power, you have many places around the world this missile could be intercepted, but it does not succeed. To deploy this missile is a new strategy that's not in the books, there is no response either. The nuclear war head mounted on the missile could even be bluff, nobody knows for sure.
Time pressure on negotiations
Suppose you have to negotiate with the aggressor. His missile flying around for a day now, during the negotiations. The aggressor has the means to challenge you with a turn-key acute threat. This nuke can (and should) be cancelled at any moment, the aggressor needs to do that. If it does not happen, you can't prevent the damage and the aggressor has not even indicated a target. This would put enormous pressure on negotiations to give in, and meet demands quickly. You'll beg them to crash this hell machine into the Pacific ocean.