When making a search on Trenitalia the number of changes, if any, is listed in the 4th column of the search results page. Or count the number of train # above the departure hour.
Regional trains have no reserved seats, so they can't sell out. But Regional ticket purchased online do not need to be time-stamped before getting on the train, it's one thing less to worry about.
Discounted tickets of high speed trains are not available on the day of travel, so in some way discounted tickets do sell out.
The Full price tickets of high speed trains rarely sell out, I'd say never on a route served by two competing companies who run 2 high speed trains per hour from Rome to Naples.
In short, You can always pay the expensive walk-up fares at the last minute, get a BASE ticket and jump on the first train departing to Naples.
As explained above, Italotreno calls the full price tickers Flexi instead of BASE: different name, better T&C if you are late, same extortionate price.