I personally would not change hotels so often. But that is a matter of personal taste. We'd rather enjoy feeling familiar in a neighborhood than cover more countries on one trip. If you are going to cover so many cities, I would consider choices that don't cover as much ground, so you spend last time on trams to the station and on the train. For example:
Each of the countries you are visiting are rich destinations that could take more than three weeks to see all of their regions. Taking nothing away from Munich, you might consider including Alsace and/or the Black Forest, and stopping at Lucerne, and flying home from Zurich. (I'm looking forward to seeing Louvre/Lens, but that's a minor destination.) I'm suggesting that there are many visual substitutes for Strasbourg, especially in Germany. But even Colmar is an adequate substitute.
You have to make choices, but it's too bad to miss the scenery in either Konstanz (or Bregenz) or Insbruck. You might check their weather records (i.e. foggy days per month) against Lucerne's once you know your exact travel dates. I'm pretty sure Rick recommends a cable car in Garmisch, but any such vista is subject to fog.
If you anticipate returning to Paris in the future, you can get away with 4 days, but that's very short. Although Paris-Strasbourg is a very easy train trip, you might check air prices to Frankfurt or Stuttgart from your home area as well.
When we were young and taking one trip a year, for example, we did Innsbruck-Salzburg-Munich-Vienna in two weeks. Alas, we still haven't been to Neuschwanstein, although we've been to Germany at least four times, and have seen many castles. Our first visit to Paris was a week there and a week in London. We didn't get close to bored, despite rain.