the house will have people in it who don't know each other, and they will have their personal possessions, documents, money, passports in their rooms.
I think they need a proper lock.
You could use a nightlatch ("yale" type) but when the doors swing shut they will automaticaly lock unless the occupant remembers to snib them back, they will need to hang the key round their neck.
Notch estimated £40 for a better rimlock, it would be much easier and more normal, I think, to have a chippy in for a day to fit mortice locks to all the doors in a popular standard size. Presumably you have thick firedoors. BS deadlocks are very widely sold at competitive prices. The latest red-case Union 5-lever is very good. You could keep a couple of spares and change them yourself in ten minutes or so with just a screwdriver when there is a change of tenant.
When the locks are the same make and model changing them is very easy.
plain deadlock
https://www.screwfix.com/p/union-bs-5-lever-mortice-deadlock-stainless-steel-2-64mm/3452d
sashlock that includes latch for operation with handle
https://www.screwfix.com/p/union-bs-5-lever-mortice-sashlock-stainless-steel-2-64mm/4458d
There are some cheaper makes, but the BS locks are built to a good standard and withstand some of the quick and easy burglarising tricks you see on the web.
If you buy a cheap 3-lever "bathroom lock" it is likely to be much more cheaply made and it will be a nuisance when it breaks, jams, or wears out.