I think this is a good point, and one I hadn't considered. I find the same thing. It may well be that any initial inflammation after insertion decreases accuracy, such that letting the inflammation subside before commencing calibration would improve early accuracy. If so, then early insertion of the replacement sensor would help.
But, the caveats: there may be aspects of Dexcom's calibration/measurement technique that we are unaware of that are an alternate explanation for higher "second Day 1" accuracy. In my experience, some sensors continue to improve in accuracy beyond day 1, implying an additional integration of data by the receiver that spans beyond the calibration period and across multiple days of measurement. In this case, given that the unit has to cope with variations not only across sites but across individual patients/users, it might retain the most recent set of calibration assumptions as the default starting condition for a new sensor. So if that sensor happens to be at exactly the same insertion site (as is true when you restart for week 2), you would expect better accuracy immediately. I for one don't know enough about how the G4 deals with data integration to say whether something like this could also be an expanation.