Italy train travel - advantages to booking in advance??

Those are primarily regional trains, so no, there's no advance discount and prices are pretty cheap to start with. Buying online locks you into not a specific train but a 4-hour time window, which can still be unnecessarily restrictive.

Check by yourself. Go on trenitalia.com/tcom-en. Discounted fares, if available are called Economy and SuperEconomy.

Regionale trains are subsidized and offer no discounts for advance purchases, but you could stumble upon one of the few Intercity trains left.

You'll have to use italian station names and enter your actual day of travel.

If you are traveling on a train that requires a seat reservation or commonly called advance reservation then there will be three levels of ticket pricing - Super Economy, Economy, and Basic. The SE and E are discount tickets will restricted and limited available. Basic is the standard walk up fare. For all Regional trains it is one price at all times and no seat reservation. And, of course, never sell out. No seat --- stand till one becomes available. Since you schedule will be Regional trains, the short answer to your question is NO.