Without judging the merits of your chosen destinations, and forced to group all your chosen destinations into the base-town travel model, and in consideration of what makes for a possible day trip... I can only offer this list of bases, in no particular travel order. Base towns are in bold.
1) Frankfurt + Cologne (+ maybe Heidelberg)
2) Berlin
3) Dresden
4) Würzburg + Rothenburg
5) Heidelberg (possibly a 1-night stop on your way between Frankfurt and somewhere else, like Würzburg or Munich?)
6) Munich + Harburg + Neuschwanstein
7) Koenigsee
8) Frankfurt for final night?
I thoroughly enjoy the base-town model and use it frequently myself. But I would label this a failed itinerary and a failed base-town strategy because the destinations have been chosen without reference to how a base-town approach might work in the real world. 3-5 base towns would perhaps be workable over 15 days. 8 bases, spread out geographically as they are, with major destinations like Berlin, Munich and Dresden that call for multi-day stays... well, you don't end up with enough time in your bases, you end up with too much time in transit... it just doesn't work. What you have is a set of destinations that lend themselves to a bus tour over 15 days.
Dresden is too major to visit on a daytrip from Berlin.
While you might be able to work in separate daytrips to the Koenigssee and Neuschwanstein from Munich, there's a disproportionately large amount of time to be spent on public transport for each day. N'stein's 30-minute tour ends up costing you nearly 5 hours round trip from Munich! If this faux-castle is a must-do for you, stay there a couple of nights and enjoy the rest of the area. Same with the Koenigssee.
A base-town approach with fewer destinations (again, without judgments about those destinations.) I would probably drop Cologne / Frankfurt / Heidelberg. Book Frankfurt at the end (for 1 night.) Details:
Upon arrival at FRA, head to your closest destination... Würzburg base (3 nights.) Day 1 is lost; 1 day each for W'burg and R'burg. (Warning...others will tell you Rothenburg cannot be visited without spending the night there.)
Dresden base (2 nights)
Berlin base (4 nights)
Munich base (3 nights)
Base in the Alps (either Füssen or Berchtesgaden/Koenigssee, 2 nights.)
Final day/night... long train trip to Frankfurt + final night (1 night.)
My personal take on your destinations: Too many large cities, not enough of Germany's natural wonders and smaller old-world places. With FRA in and out I would have my first or last base in the nearby Upper Middle Rhine Valley for at least 2 days, 3 if you really want to see Cologne. I would drop Dresden and/or Würzburg/Rothenburg. And I would opt for 3 days rather than just 2 in the Alps.