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)
If one could just walk into a store and buy plutonium, then society would probably take a much different approach to nuclear security.
Transparency doesn't serve us here.
Bioweapons do not have similar dual-use beneficial purpose as the AI does. As a result, AI development will continue regardless. It can give competitive advantage on any field.
Bioweapons are not exactly secret as well. Most of the methods to develop such things are open science. The restricting factor is that you potentially kill your own people as well, and the use-case is really just a weapon for some mad man, without other benefits.
Edit: To add, science behind "bioweapons" (or genetic modification of viruses/bacteria) are public exactly for the reason, that we could prevent the next future pandemic.
The most risky parts of biotech, the ones directly related to bioweapons, are not made publicly accessible - but it's hard, as unlike with nukes, biotech is dual-use to the very end, so we have to balance prevention and defense with ease of creating deadly pathogens.