Ha ha! Dream on.
Hence the current service to Lyon, Avignon and Marseille. Lyon is 4h45, Marseille 6h30 (both outbound) on the existing Eurostar with one intermediate stop at Ashford. The train stops at Lyon Part-Dieu for direct city access; if it went direct via St Exupéry it would be about 20 minutes quicker to Avignon / Marseille. Eurostar already do pretty well out of the existing train, however logistics are against further expansion; you need the train to do out and back in a day to make it work, and the timings are just about as stretched as they can be. (0719 off St P, 2200ish return back st St P). Also capacity on LGV-SE is at a premium, ie there isn’t any on Summer Friday / Saturdays (or Winter Saturdays for that matter).
Also, whilst Lyon is a big business centre, it is a big business centre for French Business. There are only 6 flights a day from the whole of the U.K. to Lyon outside Saturdays in ski season. For comparison, to Amsterdam there’s well over 60 just from London (plus another 5 to Rotterdam), and another 70 or so from the rest of the country. Amsterdam is a huge market, but realistically, Eurostar will struggle to fill more than the 5-6 trains a day planned. (Even then, 5-6 dedicated trains will have the same capacity as about 25-30 flights, and at 80% load factor would carry twice as many people by train than London - Edinburgh). The Lyon / Marseille market is just about covered by the existing service, and I can’t see that changing.
As I have posted several times recently (and
@Chester1 has independently suggested) the only likely further Eurostar route expansion is:
Frankfurt via Köln
Geneva
Bordeaux summer weekends
Lyon ski season Saturdays.
Frankfurt is certainly worth considering, but Rome is absolutely bonkers. It would be at least 11-12 hours - it’s 1200 miles and there’s quite a bit of it on the conventional network through the Alps. It couldn’t possibly compete on time, frequency or price.