Immersion? Well, okay then. Discarding fantasy level-based logic (which is neither logical or immersive)...
Is it silly to have a weapon strapped to your back while lying on the table? Yes, but only because that would hurt your back. The same thing happens when characters of any sort sleep on beds/bedrolls/etc though, so we can safely suppose that people in the Divinity setting have extraordinarily well-padded vertebrae and don't mind lying on such things.
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. With the collars on that danger is gone. Beyond this we have the prisoners wandering more or less freely around the ship, including one acting as a 'cook', with resulting access to various sharp and pointy things (as well as various means of setting people and/or the ship on fire). To say nothing of how easily the assorted crates, beams, barrels, braces, bottles and other glass, metal, and wooden paraphernalia could be turned into weapons on short notice if someone wanted to. And there's the fact that even without source or weapons anyone with a lick of non-Source magical talent could wreak all kinds of havoc if they were inclined. So no, someone carrying a stick isn't likely to stand out as abnormally dangerous, especially since - once again - those don't call up Voidwoken. Despite this relative lack of internal security, the Magisters are clearly in control of things and remain so until someone's collar comes off.
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.
Now, I will admit that I haven't fiddled with the new patch enough to meet Little Miss Collar-Off again, so I can only go by what has been written here about the fight, but one could reasonably suppose that she simply hasn't had the chance to store up enough Source to pull a trick like that a second time. After all, people keep complaining about the lack of source point availability on the island - why shouldn't she be having the same problem as you are?
