The trouble is that opponents can mount a response while the attack is in progress. Information asymmetries would force a defender to assume the worst once they see the first missile in the air and launch their entire arsenal before their counter-attack capability was destroyed. It becomes a feedback loop when the aggressor is forced to assume they'll be met with the defender's entire arsenal.

Fortunately this is not true. Actually destroying retaliatory capability requires a sustained barrage of hundreds of nuclear weapons, the first rocket will definitely not do it. And while a single rocket will trigger a return strike with a nuclear weapon it will not trigger an all-out response.

If you ever get the chance to read old declassified nuclear attack plans against a city, you will see the same. A single nuclear weapon ... just doesn't do it. Those plans involve starting out with something like 10 nuclear explosions (not even directly against the city itself, rather on supporting infrastructure), and then one more every hour or so for 48 hours or even weeks (these plans are/were made for most large cities, and even for US cities where the likely plans for Russian nuclear attacks are created by US to allow for better preparations).

In some ways what you see in the first episode of Battlestar Galactica is somewhat accurate. First, dozens of nuclear explosions make an effective response impossible (e.g. military installations, runways, important bridges, train lines, communication, ...), then a methodical "sweep" with nuclear explosions of the entire city. This cannot be done with one, or even 10, nuclear bombs.

And even pretty bad radar systems can tell the difference between one and tens/hundreds of rockets.

So whilst this is a concern, it can and is eliminated with proper infrastructure and planning.

There will not be information asymmetry once a nuclear attack actually starts happening.

That's not how these systems work, at least in the US and Russia. "The Doomsday Machine: Confessions of a Nuclear War Planner" by Daniel Ellsberg (who was involved in war planning before he leaked the Pentagon Papers) has some fascinating and scary info about this.

Apparently there are backup systems in both countries that will fire nuclear weapons automatically (!) at predefined targets if certain cities are hit with nuclear attacks - e.g. Washington, Moscow, etc.

That's why deterrence is effective - because any strike can automatically lead to hundreds of millions of people dying (and, if the modelling of nuclear winter is correct, potentially pretty much all large mammals within a few years)...

The point is more about even countries with a minimal nuclear arsenal being in relatively equal military footing as the countries with large arsenals because no country seems willing to risk losing one of their major cities to nuclear attack. So, threatening 100 cities is about the same as threatening 1 - no one will attack you.

That's pretty much the main reason north Korea hasn't been attacked since the Korean War: even without nuclear weapons, nobody wants to risk war when Seoul is all but guaranteed to be leveled.

Why just 1?

It was an example to show how a country with a chance of landing even 1 nuclear missle successfully is on equal military footing with a country that can land hundreds assuming the stronger country does not see losing any of their cities as an acceptable risk.