My hypothesis is that making the knowledge of how this stuff works accessible to the public results in a lot of false-positives (from people just playing around) that intelligence agencies have to then sift through / tune filters against; which creates a noise floor for real foreign nuke programs to hide in.
So governments ban anything that could result in false positives (since nobody needs to be doing any of that stuff outside of designated labs anyway), to lower that noise floor; to in turn make catching the foreign nuke programs tractable.
(It's a bit like how fancy mansions always have a completely flat and barren part of the property between an outer perimeter and the start of any gardens/outbuildings/water features/etc. That barren area is a killbox: since nothing is supposed to be there, anything at all that does appear there is a valid target for the manion's guards to shoot at [or otherwise engage with], without needing to get a clear identification and command approval first. This wouldn't work if the killbox was covered in vision-obscuring decorative features; nor if the mansion had employees, animals, etc. that had a valid reason to wander into the killbox. So such things are prevented, in order to make the problem of perimeter security tractable.)
But this knowledge is readily accessible today. At least for manhattan-project level bombs. For later developments you mostly get simplified overviews with important details left out. But even there you have communities speculating about this very publicly
The same is true for adjacent topics. Most LLMs will refuse to tell you how to make dynamite, youtube demonetises any videos about it, but it's right there in the wikipedia articles on dynamite and nitroglycerine
Administrative convenience is no excuse to limit individual liberty, capacity, or knowledge. Individuals come before states!