The spots in the Maritime-Alps in France that I've enjoyed like no other cannot be reached by public transit. (Single-lane mountain "paths" blocked by goats and only one way up and one way down with no room for a bus to turnaround come to mind.) And such places and many others can only be leisurely explored by car. And Switzerland, famous for its "connectivity", would have required "timing" in order to get to half the mountain spots I loved and many of the places that may have been reachable by public transit would have required "timing" and then hit the schedule or miss it.

For city center to city center in a constrained geographical area, nothing beats public transit from convenience or cost perspectives and Eurail may be perfect. However for multiple city centers across several countries and the country side .... only a car will get you to many spots and enable you to stop at your leisure for your leisure without worrying about a "schedule". (A bus may work for some of the places, but the rail will not work for all.)

To hit the places named by the OP, a Eurail pass would be $1200 to 1880 to cover two persons and that is only up to a maximum of 15 days of travel. I guess that could work, but if three or more persons are travelling together, then the value of Eurail rapidly becomes less competitive than a car, even factoring in "convenience". And if one wants to enjoy the countryside, trains just don't do it completely.

Last time I looked at Eurail passes -- 2003 and 2004 -- the final calculations for the itineraries I was interested in that helped three people hit such a wide geographical area -- including comparable hotel quality, places seen, time in city center and at sites, costs of accomodation, costs of transportation -- a car was a better total value on the cost side. Maybe fuel prices would wreck the accuracy of the prior calculations and the two travelers changes the equations significantly enough, but that depends on how extensive the OP would like their travels.

In any event, I'd never give up my love for alpine driving and more rural spots, so maybe that "clouds my judgment".

[It's pretty much agreed upon that LCC flights are not economical for so many city center to city center and other travels -- unless doing laundry en-route is an option and baggage won't exceed the miserly LCC limits.]

It does come down to some sort of cost vs. convenience balance, but if the car is used for airport (-area hotel) to airport (-area hotel), the convenience is not sacrificed and the cost is the same or less. But if money is not the limiting concern and cities are the only interest, then city center hotels and a combination of public transit and flights would help. With the rental car, one issue that can wipe out the economics of that option is a non-circle-type trip (since out of country drop-offs are much more expensive).