Also what is the best European boarder for the empire in the long run? And borders in general?
I still believe, that the Elbe border, perhaps including Marcomannia up to the Sudetes and Carpathians is the better border. Not because it is much shorter. Actually it is not! And surely not because Germania is wealthy, easy to romanise or free of trouble.
But because more germano-romans are longterm beneficial to the empire. And most importantly, the dangerous free german population is reduced by perhaps more than 50%. And also very important: this infertile land makes a perfect buffer zone and battlefield to avoid any destruction to the wealthy Gallia and Northern Italy. Exactly like Augustus' initial plan, before the pannonian revolt throwed it over.
A roman Germania Magna would also avoid german piracy (starting soonly later in the mid 1st century AD) and better secure Britannia this way. Well, the much better idea and very shorter border is of course to never invade Britannia at all!
I do not believe, that a roman empire up to the Elbe would be overstretched up to an extent, that it becomes ungovernable, just because of one province more. If historians talk about a too much overstretched empire, they usually do not mean the geography. They are talking about the political dimension of this huge empire. A few more provinces in the north are not changing or escalating the fact, that the roman empire was already overstretched since the 2nd century BC. So how to avoid overstretching the capabilities not just of an ancient republic but also of an ancient monarchy?
The much more interesting question would be about the best eastern border of the Empire! And if you expand here to a reasonable extent (eastern Zagros Mountains), you do overstretch the empire definately. Again not that much geographically, but politically. And in this case also culturally with fully unknown ramifications.
Of course you do not need a son of Augustus to let a roman emperor get the idea to march back to the Elbe. The more interesting question is, why should a son of Augustus or any other emperor get this idea? He could not know, how important these germans would become 2-300 years later.
And the funny thing is. Just a border up to the Elbe in the North and the Zagros mountains in the East would not avoid the Fall of the Empire! Because it is already politically overstretched. With or without Germania. The external threats are just one half of a medal called the Fall of Rome. The easier to solve and way less dangerous half! From an intellectual point of view it is the much less challenging part.