Even if such a "smallish" 1 km asteroid hits, in general everything will change. For example, the asteroid could still cause enough chaos to weaken a country or countries, opening up for opportunistic wars. Since the long-term effects of a non-ELE would be transient, some countries might want to take advantage of this situation and invade (resource grab or glory for motherland or righting old wrongs or something). And then, what things would be seen next - for this we would be in unknown territory.
Even without an outright war, the number of displaced people could become very large. People would likely not sit still and clean up, but try to move away. Can the receiving end handle that many people, can they move enough help in when the just-in-time supply chains are disrupted to pieces? If not, there will be a collapse into some form of chaos at the receiver. And again, people might move, etc.
For an ELE, an offworld base is the only option for continuity. If that is not in place when an ELE hits, then humankind will be dead.
A Mars/Moon base operating at large enough industrial and R&D capacity (akin to a small to medium sized country) could help restore normalcy even without an ELE.
So, I think an offworld base is required anyway, even if we don't sweat so much about 1 km rocks, but still want to be serious about protection against an ELE.
Though the direct effects would be mostly local, the systemic effects would reverberate globally since in the modern world things (such as food production, supply chains, etc.) are so meshed together.
Draw a 300 km circle at your chosen impact point, then say bye to everything inside the first 150 km. The rest of the circle would be damaged to a varying degree. You can easily find places for impact points which, although not an ELE, would still turn many, many people's lives nasty.