Your France journeys may be in jeopardy because of the rail strike.
"Neither side appears ready to back down, with Prime Minister Edouard Philippe warning that the government would not be deterred despite union pledges for three months of rolling stoppages, and possibly more."
I would NOT buy a Eurail pass NOW in any case. If you decide it's worth it, buy it in July once the strike has had a chance to play out. You may have a change of plans between now and then anyway.
I'll take a look at the options for point to point tickets below for a few of your legs...
AMSTERDAM TO COCHEM: I checked the German Railways site just now for July 26 - there's a €19.90 fare available for pre-purchase.
COCHEM TO BACHARACH: €22, normal price at German Railways
BACHARACH TO BADEN-BADEN: €19.90 fare available for pre-purchase at German Railways.
SWITZERLAND: I'd drop Zurich and Lausanne, probably. Yeah, it's expensive. Let's say you finish with Colmar. From nearby Freiburg, Lauterbrunnen is a 3.3 hour train trip, but you can pre-purchase tickets cheaply. Current price is 19.90 at the German Railways site for a morning departure on the date I checked (Aug. 2.) You want to see Bern? Just do that on the way to Lauterbrunnen - it will cost you nothing extra to look around Bern for 4-5 hours. The German Railways site has a stopover feature - you input Bern as a stopover and the amount of time you want there.
So do you kinda see where all this is going? That rail pass is likely to cost you much more. The advance-purchase tickets do ask you to commit to a specific train on a specific day - but it looks like you are planning day to day and have some budget concerns, so they might be a very good trade-off for you. Note that there's a fee for refunds.
You can check the French, Benelux, and Swiss sights on your own - but I'd start with the man in seat 61 for the best tips.
BADEN-BADEN: A place the geriatric upper-class European elite like for gambling and spa treatments. Its train station is a long bus ride from town, so it's a poor place to use as a travel base. I much prefer Freiburg or one of the smaller Black Forest towns.