DAVdroid detects read-only calendars and marks them as read-only in the Android calendars provider, i.e. calendar apps should not be able to add events to these calendars. However, this detection is done when the local calendar is created, which is when you add the account.
Can you please delete the DAVdroid account, add it again and see whether the calendar has a “read only” icon next to it? In this case, DAVdroid has detected that the calendar is read-only and should mark it as such.