I moved from my parents house which had a tumble drier, to my own, which does not, and took a bath sheet with me and bought the rest new.
Because the old bath sheet had previously been tumble dried, it became dry and scratchy and cardboardy when i dried it over the clothes line/radiator, whereas the others didnt.
I think if they have never been tumble dried then they dont need it to stay soft, but if you have ever tumble dried them then you need to keep doing it to keep them soft