Second, while I agree that there's a problem here, the DOJ doesn't simply want "warrantless access rights" to "most US email". What it's claiming is more subtle: that mail that is older than a certain threshold and that has been open requires only a court order, and not a bona fide search warrant.
Edit: To your main point, I think your emphasis on the fact there is still a court order is misplaced. Of what practical value is a court order if there is no burden to show probable cause (instead only 'relevance to an ongoing investigation'), and you have no opportunity to challenge (or even know about) the order. How many requests under such a standard do you really think are going to be turned down?
For a simple court order (which would just be an order to hand over something) they only have to demonstrate suspicion.