Not so far away
"Taking a larger perspective, both trains are going to redraw the travelers mental map of Italy. Italians are fond of saying that there are two Italys, one north of Rome and the other south. Theyre now a lot closer; Naples is no longer way down there. The Italian government may have laid down more than track."
When Japan introduced the shinkansen, it had the effect of virtually shrinking Japan. Suddenly Yamaguchi and Aonon were "close". Where as before, it took 10 days to make such a journey, it suddenly took less than 10 hours. Now it can be done in less than 5. Europe is seeing the same thing happen. It's now possible for a Londoner to easily spend a weekend in the Alps without spending the weekend getting there.
But a big problem which JohnMcGrew identified is that too many people, especially politicians, confuse HSR with commuter trains. Every politician wants their little town, village, or cross roads as a station on the HSR, expecting big things if they can pull it off. But if they succeed short term, the line ceases to be HSR, thus meaning that they eventually fail long term. The only way to run an HSR is between major cities, the equivalent of LAX to SeaTac in under 2.5 hours without needing to go through airport security and at a fraction of the cost.