The ship isn't comparable to a modern prison bus and it's only somewhat comparable to a prison ship. That the magisters are really only concerned about Source is established early on - Source calls up Voidwoken. Swords don't.
Magisters are concerned with Sourcerors being allowed to roam free attracting Voidwoken which causes chaos. That is the entire point why they are all being forcibly rounded up. To get them to the island away from everyone else.
Allowing prisoners on the ship to have weapons does nothing to help the Magisters get the prisoners to the island, and poses a risk to getting prisoners to the island. Therefore, allowing prisoners on the ship to have weapons has no justification.
Magisters might pretend for the sake of appearances that the prisoners are not really prisoners, but they are.
And I would personally find it immersion breaking that - despite the ready-made weapon materials lying around everywhere - your character is magically without and unable to create or obtain even the most improvised of Wimpy McStarter weapons until they suddenly need one (the abovementioned collar-off incident), whereupon presto! - a crate of them just happens to be right when and where the PC needs it! Umm, yeah. Immersive that is not.
What, so for you, Magisters keeping a chest full of confiscated items/weapons in the back room away from prisoners makes
less sense than letting prisoners walk around armed?