8 Day tour: Rome to Barcelona, skirting the Med Sea?

I think this is feasible for nimble travelers and the idea of a whistle-stop train tour has a lot of charm.

I would probably consolidate some of these destinations, however; either the French or the Italian riviera, but not both, certainly Arles over Marseilles, and I might skip the Costa Brava overnight.

This would allow more nights in the remaining destinations. But that is really a matter of personal taste.

First....no, because of your second point.
Second....way too many stops for only 8 days.
Third....such an itinerary is best by car. Train connections between Italy and Spain across southern France are very poor. They'll spend at least 20 hours on trains, cutting a whole day out of their vacation. However, they'll take a major cost hit renting a car in one country and dropping it off in another.
To be honest, with 8 days, I'd be more likely to spend 4 days in Rome, with optional day trips to Florence and/or Pompeii....and four days in Barcelona, with optional day trips from there. You can fly between the two cities cheaply on airlines like Vueling and, less conveniently, Ryanair, if you book well enough in advance.