My advice: Do some research beyond the very patchy Germany advice you get from Rick Steves' materials. Bacharach, Rothenburg, and Füssen themselves are of very minor importance, so take another look at what's actually BETWEEN Frankfurt and Munich. Start with mchpp's and TC's suggestions... Würzburg, Bamberg, Coburg (Castle) and Nuremberg. These are well-known destinations for European travelers with things to see - including UNESCO World Heritage sites - that will charm your socks off. I would add BAYREUTH to this list (incredible opera house) as well as REGENSBURG.
From FRA it might make sense to head straight to Würzburg. The direct train trip from the FRA terminal takes 1.5 hours. Easy. By the way, Würzburg has river cruises along the Main River beginning in April.
https://www.mainschifffahrt.de/
I would also look at the places below as well, smaller towns where you will find the half-timbered architecture similar to Bacharach's (which is very attractive for sure - but there's really very little else to DO in Bacharach but relax.)
Iphofen, an old-world town for wine and art lovers, Riemenschneider works, and right on the main train line between Würzburg and Nuremberg.
Scroll through these pages for more Iphofen photos. Like Rothenburg in some ways but without the tourist throng.
Marktbreit, Ochsenfurt, and Sommerhausen, just outside Würzburg on the Main River. This older video captures all three. The filmmaker, one of my favorites, seems to regret using the car to get to these towns, which are easily accessible by public transport if you are staying in Würzburg for a few days.
There is a theme route within Franconia called the "German Timber-Frame Route" with lots of half-timbered buildings that lists some of these places and others as well. The page is in German, but you can use the list of towns for some google-work.
https://www.deutsche-fachwerkstrasse.de/Regionalstrecken_Staedte/Franken.html
One of the towns - Bad Windsheim - has an excellent outdoor museum where you can explore local life over the last 500 years:
https://www.tripadvisor.com/Attraction_Review-g198421-d284746-Reviews-Frankonian_Open_Air_Museum-Bad_Windsheim_Middle_Franconia_Franconia_Bavaria.html
I've visited all these places using the train system. Nuremberg makes an excellent travel base. Stay there for a few days and you have a wide selection of places to visit on day trips by train. Rothenburg is less than 1.5 hours from Nuremberg. Day trips to the other places are typically shorter than that and often direct. You can see why Nuremberg makes such a good base with the map below, which shows almost all the towns I've mentioned:
https://www.vgn.de/media/verbundgebiet.pdf/
I'd probably arrange the trip as follows.
(FRA>Würzburg (1.5 hrs., direct train.)
Würzburg base (2-3 nights) (+ visit Rothenburg, Marktbreit, Sommerhausen, Ochsenfurt, Iphofen?)
(Direct train from Würzburg>Nuremberg = 1.25 hrs.)
Nuremberg (5-6 nights) (+ visit Bamberg, Coburg, Bayreuth, Erfurt, Regensburg, Bad Windsheim, Timber-Frame Route towns)
(Direct train from Nuremberg>Munich = 1.25 - 2 hours depending on choice of trains.)
From your bases, just play it by ear, day by day. Do museums if it rains. Leave out places that don't interest you, see the ones that do. Buy day passes as you go (cheap in this area.) No tight schedules, easy-going sightseeing.