There's are real concerns, but I feel like we are only formalizing the status quo.
Throughout the Cold War, it would have been fairly easy to kill the other sides leader, especially if you are willing to use a nuke. I still thank that is true. The president's travel schedule is public, and its not like he's always within 15 minutes of a nuclear bunker. The reason countries don't assassinate each other's heads of state is not because they are unable to.
If you live in Manhattan or Washington DC today, you basically can assume you will be nuked first, yet people live their lives. Granted people could behave differently under this scenario for non-logical reasons.
Given you could use a conventional, small explosive, that makes it easier, but my guess is it still does not work. There are at least two big issues:
I thought about something like this (A nuke near the White House) but quickly realized the bomb would have to travel with them. There's just no way to make it secure enough with the travel schedules such people have, and the adversary's inspectors would have to follow them around to enforce it so there's no privacy either. Not to mention all the world leaders occasionally gather in one place, which raises the danger even more.
If you can strike in a way that prevents retaliation that would, by definition, not be mutually assured destruction. Your understanding is also wrong, at least for most of the cold war. Nuclear submarines make it impossible to strike so hard they can't fire back, and they have been around since 1960. People in the cold war were very much afraid of living in a potential target area, but life went on.