Thanks you all! I read somewhere that lophophoras need smaller pots due to the fact that they are somewhat rot-prone. I'm not sure what the logic is behind that. Can someone elaborate?
I put some of them in a very big pot months ago. It seems those are quite a bit softer.
I'm still curious about watering. I got gritty media and clay pots. After watering, the pot and soil seem to dry up in 2 to 4 days. Perhaps that accounts for how frequently my cacti can (or must?) be watered. Can drainage ever be too good for cacti and succulents?