I think it's actually the opposite. The US stockpile consists of mostly (entirely?) thermonuclear weapons. They're smaller for a given yield, and are therefore much easier to deliver. Most of them are also variable-yield, so you can still use a hydrogen bomb to make a smaller boom if that fits your strategic goals.
Edit: it looks like this is the case for the other superpowers as well. The only nuclear state for which this may not be the case is Pakistan, although it's possible that they have a boosted weapon of some sort.
Some of the scenarios I outlined—rogue non-state actors, regional wars—may lead to isolated nuclear attacks but not full exchanges. I’m not sure if the hydrogen bomb distinction is relevant here.
(Yes, afaik what you say is true, but I think this is sort of a red herring.)
I think that a terrorist attack with a nuclear weapon would be less likely to trigger a world ending counter attack since there is no state to target.
Therefore, I think it's possible that while the chances of a nuclear attack have gone up, the chances of nuclear Armageddon have gone down.
However, I am definitely not an expert so I may be mistaken.