I would be surprised if this hasn't already been requested, but some quick searches didn't turn anything up.
I want to enter tasks that have only a start date and no due date. As an example, I have a task where I check my tire pressure once a month. I would like to set this with a start date, no due date, and have it repeat monthly from checkoff. Why? Because it's not really due any particular time -- that field makes no sense in this case. The other reason is that I don't want to see the task at all until the day it's time to think about doing it again. If I set a ">" due date the task starts showing up a week early and since I have a lot of this kind of thing it really clutters my task list with things I don't really care about. It also messes up the importance levels since due date is a prime factor in that calculation, and as I said these are not items that really have a due date.
(In any case, the behavior of repeating-from-check-off events with no due date is currently pretty screwy in m opinion. A due date gets created when the event is checked off the first time and the start date is bumped forward by the amount of the repeat with the check-off date not taken into account.)
Right now I can get around the problem by setting both a start date and a >due date but that's annoying (and doesn't make sense), particularly when I'm trying to do something fast using the awesome iPhone app.
You are correct. A repeating task repeats from the due-date. If the task doesn't have a due-date, it is assumed to be the day that it was checked off. Currently there is no way to have a task repeat from the start date, but I see your logic and think that it is a good idea, so I'll add it to our todo list.