Since start date and due date are joined as "Dates" on the task view, it would be nice to have the same as a list column. I wouldn't mind if it was read-only.
I don't have that many start-date-only tasks, so I don't have a dedicated start date column on my today task card (or at least the column is cropped out), but then if a recurrent start-date-only does come up, I have no context on why it's there (there's no recurrent icon on due date if due date isn't set either, which I think is ok)