Yes they could... but replacing a lockset in an existing door is very simple... and cheap. Door locksets typically come in two sizes.. 2.5 inches and 3.5 inches... I'd expect every door to already have a lockset mortised into it.. all they have to do is take off one handle, take off the lockset, replace the lockset with a new one valued at 10 to 15 euro, re attach the handle.. door is now lockable and all keys are accounted for. Shouldn't be too hard, easier than changing a plug really, less physical dexterity required.
It could be that no-one is allowed make any modifications to a house but that seems unreasonable to me... I would refuse to live in a shared house if the doors weren't lockable but I suppose you could vote with your feet and refuse to rent such a room.
I don't think the landlord is liable for tenants property (for reasons outlined already)... so the only hope for the tenants is to have locked doors.