Because decapitation strikes are too easy, or at least too dangerous. A large country can mitigate this threat through dispersal of strike/retaliation capability, and by building early warning systems. However, early warning only really works reliably when a strike can be detected a substantial amount of time (“a few minutes”) before it takes effect.
This is the logic behind bans on orbital weapons (de-orbiting weapons given less warning than ballistic weapons) and on the mutual withdrawal of nuclear weapons from Cuba and Turkey at the resolution of the Cuban Missile Crisis. This is also the game theory logic behind countries like South Korea and Taiwan effectively outsourcing their nuclear deterrent to the United States. In The Dead Hand, David Hoffman quotes Zbigniew Brzezinski as saying that after detection, initial cross-checking, and message delay, the President has about seven minutes from launch to impact of a Russian (Soviet) ICBM to decide whether or not to order retaliation. That window might have gotten slightly larger since the 1980s, but not by much. The United States’ (and other existing powers’) nuclear strike capability is sufficiently dispersed not to be neutralized by local subterfuge, and highly likely to survive a a first strike. This further reduced the likelihood of a launch on false-positive early warning.
The leader of a hypothetical nuclear South Korea might have only seconds (i.e. no time at all) to decide on response to an incoming nuclear attack. Any credible response would either have to assume being hit or function automatically (e.g. the national leader would have to delegate launch authority). The Soviet “Perimeter” system did allow this delegation for the reasons outlined above, but was not always active. Perimeter was, however (again, source is Dead Hand) intended to launch only after hit from a first strike. So if the Soviet leader had a warning of incoming, he could safely activate Perimeter and trust that Perimeter would only trigger a Soviet launch if the USSR was actually hit. In the Korean case, to be effective given the low warning window, the decision to activate the retaliation system would either have to be made ahead of time or effectively happen automatically on launch. Or, South Korea could just assume the risk of decapitation — not something other nuclear states do.
The situation is even worse for a city state, in which decapitation from a first strike is very likely (because of the small territory), and warning times are lower (same reason). Worse, basic assumptions used by current powers about likely origins of incoming attacks won’t hold — an attack could come from any direction in a world of nuclear sovereign small states. Since decapitation is a likely effect of a successful incoming strike, the only two options are launch-on-warning or outsourcing retaliation. The former would mean lower launch thresholds and less (quite possibly zero) real-time human decision input than any current or past nuclear deterrent framework.
Outsourcing retaliation to other states gets us pretty close to the familiar world of Warsaw Pact vs NATO. This obviously involves a loss of sovereignty no matter how nice everybody tries to be about it. Managing such an agreement among true equals rather than along an obvious hierarchy would be difficult. States might exchange “embassies” that include nuclear launch facilities. They would need networks of such exchanges in order to lower the effectiveness of subterfuge. The point of such an exchange would be to reduce the need for automation of launch decisions, so there wouldn’t be a place here for some sort of automatically-enforced “smart contract” between the parties.
The other outsource option is extraterritorial, such as a ballistic missile submarine (boomer). A city state would need three boomers to maintain a minimal continuous deterrent. The expense would be ruinous, although perhaps in the future a city’s GDP would be high enough to support three state-of-the-art missile subs, with some construction & maintenance overhead shared trustlessly. Communication with the sub would be both more difficult and more important than under current conditions; the deterrent won’t work if the home state can be plausibly decapitated without telling the boomer who to retaliate against (which, remember, can’t be taken for granted in this world). An orbital second-strike facility looks much more attractive. Perhaps this will be the job of the state’s space force.
Inky
Plausibly, a situation may exist when the launch wouldn’t be detected at all — because there won’t be one. In a situation of a city state (say, Singapore) when all of the territory is highly important and irreplaceable, nuclear sabotage seems a terminal danger. Such approach also vastly simplifies and compacts the weapon — without the rocket part, the whole device can fit into a standard container. An attacker doesn’t even need to enter the security perimeter — the blast immediately outside of it (outside of the hypothetical “city wall”) could be almost as devastating. Well, destruction-wise it will have less impact, however the territory will be heavily contaminated.
Harbor cities are at even greater risk, as controlling the waterways is even more difficult. And a hypothetical device could be delivered into the harbour, dropped onto the bottom and lie in wait for years. Triggering it without attracting attention could be tricky though.
Such scenarios also make very clear why all of the nuclear powers are so wary of nuclear proliferation.
sfoil
I had a covertly-emplaced bomb in mind when I wrote about the warning time for an incoming attack being zero. “Launch” is just a shorthand. Of course, covertly setting off a single bomb probably won’t decapitate any existing nuclear power but it very likely would for a city-state. Both launch-warning converging to zero and decapitation probability rising towards one both push “launch” (general sense) thresholds down. Hence the need to disperse retaliation capability. But yeah, this and loose nukes are the “good” reasons not to let states like Taiwan get the Bomb (the bad one being that status quo powers like having status quo power).
Actually I think the most dangerous thing about covertly detonated nukes isn’t the zero launch warning (which can be understood pretty easily) but deniability. I briefly talked about that in the last paragraph but on reflection it’s a bigger problem than the sub captain not knowing where to aim; nobody might know where to aim. My guess would be that even if the current nonproliferation framework completely collapses and Monaco and Singapore nuke up, successor organizations will maintain records of bomb “fingerprint” characteristics and nuclear producers will voluntarily participate because the negative payoff to a false attribution are so high. This also implies a norm of producers held to strict liability for the use of their bombs outside overt, externally-registered chain-of-custody transfers.
I drafted a post about what it would take to turn a modern city into a serviceable “fortress” after another post but never got around to finishing it. I suspect that an external ground burst wouldn’t pose an existential threat to a syndicalist fortified city-state given a reasonably sturdy wall and the detonation standoff implied by a cleared field of fire. It would hurt but it’s probably not a serious decapitation risk.