It's all in the rates. Very few rate classes at Hertz (or anywhere else I've checked) go beyond 2 or 3 extra hours before getting to the extra day amount. That Avis rate you're talking about would likely be the same if you kept it fully 4 days.

A rental of 4 days vs a rental of a week is a tossup in terms of how often which one is less money. In this case, a whole additional week is less money than 4 days. In some cases, 4 days is less money than a week. Depends upon rate class, car class, phase of the moon, etc.

Note that if your rental were ONLY 4 days (rather than a week plus 4 days), you might be forced into a 4-day rate even if the week is cheaper. (That is highly unlikely though unless the 4 days are midweek.) Because you already have a week, the system will give you a second week rate if that is cheaper than the 4 days.

The upshot is, you know you could stay for yet another 3 days at the same rate, if you wanted.

Or, the other upshot is, the non-Dream Car rental for your additional days will be a lot less money, even if you also get that one from Hertz rather than Avis.

If you want to test my theories, price a standalone rental for the Dream Car for those 4 days and see what kind of rate you get. It would be interesting to compare that price to the price of adding them to your existing res.