> you don't put a nuke somewhere to kill people; you put it there to destroy infrastructure. More specifically nuclear missile silos, and bomb shelters (well, the people inside them.)
It depends.
"Counter-force" strikes aim to destroy the ability to respond or attack with nuclear weapons, not infrastructure per se. So that's just silos, warhead storage sites, submarines in port, airfields, etc. The US is doctrinally counter-force for about half a century. This doctrine is also reflected in technological choices: lower yields and higher precision mean lower fallout, collateral damage, and fratricide when hunting for silos, but aren't that useful for city busting.
"Counter-value" strikes are pure destruction of cities and killing of people. Russia seems to have this doctrine [1]. This is a very inflexible doctrine, because you can't credibly threaten to execute a counter-value attack on the US over things that don't seem to be worth a response in kind (like a defeat in Ukraine). It's much cheaper though.
> The very latest US ICBMs are suspected of having sub-100m CEP
Apparently the precision is good enough for photos like the one on page 23 here https://www.osti.gov/servlets/purl/1557069
[1]: At least strategically. There is a hybrid strategy of targeting military-related infrastructure, which Russia seems to have adopted for less-than-strategic forces according to recent leaks https://www.ft.com/content/237e1e55-401d-4eeb-875b-03fe68f81... .