Except for the possibility of impaired driving on Day 1 it's surely feasible. I probably wouldn't want to pay the car drop-off fee that one normally pays for dropping in a different country. You should probably look into that first.
2 nights Rothenburg (maybe 1 and add the day to Bavaria area) 3 nights
Munich/Bavaria area (arrive after Octoberfest to avoid costs and
crowds). More interested in the countryside.
You probably shouldn't mention or consider Munich if you are interested in the countryside. Munich is a large, spread-out city.
Rothenburg doesn't require a lot of time.
The "Bavaria area" is bigger than you are imagining it. It's not just a small area around Munich - it's huge - and you will cross into Bavaria very soon after leaving the "Rhine area" (which is in the "Rhineland Palatinate") for Rothenburg. Here is a map of Germany showing Bavaria in red. And here's a map of Bavarian cities and towns.
We have always rented cars in Europe and have never used the train
systems. I guess we always found the car more flexible and it allows
us to go off the beaten path.
Your itinerary is essentially the beaten path. I would look around a bit more before you start booking rooms. If you want to go OFF the beaten path, consider your itin. a first stab, and do some more research using other materials besides Rick Steves'. EVERYONE knows about Rothenburg (which exists now only for tourists) and the Romantic Road, and that's where you'll find everyone. Not that these are bad places. But they are not "the road less traveled." There are MANY nice and interesting places between the Rhine and Austria that you can explore. You should find your own, based on your own interests; they won't be unknown or tourist-free places of course - just a bit less well-known. Here are just a few examples of places that aren't "front-and-center" in the typical guidebooks.
Miltenberg - and a visitor's guide.
Mittenwald - and a visitor's guide
I hear statements like yours about cars and trains quite often. But it is not possible to draw conclusions about the flexibility or inflexibility of train travel when you've never done it and don't understand how it's done. I have to assume that the opinion is based more on one's love of driving than on the reality of train travel in Germany (which is extensive, efficient, and inexpensive - and also offers lots of flexibility.) And that's fine - if you enjoy driving, do what you enjoy. I've driven in Germany, but the rail system is so good that I now do all my exploring by public transport (which has taken me to the places above as well as many others.) Also worth noting: if you enjoy beer/wine, you have the flexibility to come and go at will on the trains. DUI thresholds in Germany are very low.