Not saying I agree that being closed source is in the public good, although one could certainly argue that accelerating the efforts of bad actors to catch up would not be a positive.
Not really. It slows down like security over obscurity. It needs to be open that we know the real risks and we have the best information to combat it. Otherwise, someone who does the same in closed matter, has better chances to get advantage when misusing it.
Nuclear capacity is constrained, and those constraining it attempt to do so for reasons public good (energy, warfare, peace). You could argue about effectiveness, but our failure to self-annihilate seems positive testament to the strategy.
Transparency does not serve us when mitigating certain forms of danger. I'm trying to remain humble with this, but it's not clear to me what balance of benefit and danger current AI is. (Not even considering the possibility of AGI, which is beyond scope of my comment)
It's not because of arcane secrets that so few nations have nuclear weapons, all you need is a budget, time and brilliant physicists and engineers. The reason we don't have more is largely down to surveillance, economics, challenge of reliable payload delivery, security assurances, agreements and various logistical challenges.
Most countries are open and transparent about their nuclear efforts due to the diplomatic advantages. There are also methods to trace and detect secret nuclear tests and critical supply chains can be monitored. Countries who violate these norms can face anything from heavy economic sanctions and isolation to sabotage of research efforts. On the technical side, having safe and reliable launch capacity is arguably as much if not more of a challenge than the bomb itself. Logistical issues include mass manufacture (merely having capacity only paints a target on your back with no real gains) and safe storage. There are a great many reasons why it is simply not worth going forward with nuclear weapons. This calculus changes however, if a country has cause for fear for their continued existence, as is presently the case for some Eastern European countries.