Yes, you can choose when you order online.

The Interrail Germany Pass is only available as mobile ticket. Paper Passes can be bought on large International railway stations across Europe. As we sell our Passes online, I cannot inform you on where and which type of Passes are sold. 

You still can buy them as paper pass via Bahn.de or at German Ticket office on major stations called "DB Reisezentrum" 

On the bahn.de website you have to know where to look. On it's Interrail page, DB now refers to bahn.interrail.de but it seems you can also still order via:

https://fahrkarten.bahn.de/privatkunde/shop/shopstart.post?GroupId=506

It should also be possible to oder via the DB phone service at +49 30 2970 (available 24/7).

Ordering via DB means the postage charges are lower (EUR 5.90).

Any specific reason not to offer this pass as a paper pass, unlike the global pass?

It is in line with our focus on the mobile Pass, but other than that there is no specific reason. If a paper Pass is preferred, it can be purchased from DB, SBB and ÖBB.

Well, only if you live near a ticket office that actually sells them (and their number is reduced each year). And as long as the app is still in beta test, my opinion is that other options should not be limited.

It would be interesting to see how many people actually prefer using the app or a paper ticket after having gained experience with both. There are multiple reason not to want the mobile version, some of which you only discover after using it.
I also just noticed that on the page comparing the mobile and paper passes, it is not mentioned that using a mobile pass on a night train may main you'll be woken up at each border crossing:

https://www.interrail.eu/en/interrail-passes/interrail-mobile-pass/mobile-vs-paper

Thanks for your feedback. I will pass it on to the relevant team. If we see more customers wanting to Germany One Country Pass in paper form, we will reconsider and act accordingly. 

This Pass is an exception as for other Passes we still continue to offer the paper Pass :)