The consensus seems to be is that Florence and Rome would make two attractive additions post tour. For me - the train seems the most obvious choice. Both have over 50 daily connections - some quicker then others. My question - is there any reason one should actually reserve tickets much in advance? It appears that by waiting - one can better decide which times would work best. Correct - or all wet? I have a special gift for missing the obvious. Than you. Again.
Are you going to spend any time in Milan? When are you traveling?
Your guide will organize the exit strategy for the group based on who is going where - either by assisting with purchase of train tickets from Orta to Milan (no station in Orta) or organizing shared taxis/shuttles and grouping people together who are going to the same location in Milan. For onward travel, if you do book ahead for Florence (probably better homeward flights out of Rome), I'd probably give yourself time and book for early afternoon so you are not rushed getting away from Orta.
That doesn't answer your main question as to whether to book ahead, though so I'll let those who've done Italian trains more recently answer that.
I believe this train requires a reservation with a pass or a point to point ticket with a reservation. Why gamble? It is impossible today to predict the availability in the future.
is there any reason one should actually reserve tickets much in advance?
The main reason to get tickets in advance is to grab one of the discounted tickets and save some money. These tickets are capacity controlled and usually are not available on the day of travel.
The main reason not to purchase in advance is the lack of flexibility: Discounted tickets can't be refunded and changes are restricted.
The top, on-day prices are always displayed in advance both on trenitalia.com and italotreno.it. No surprises: the price of flexibility is there to be calculated. Make a fake purchase on trenitalia.com, putting next Monday as day of travel: the cost difference between BASE and Super-Economy tickets is the price of flexibility.
There are only reserved seats on high speed trains and, on official sites, the reservation is always included in the ticket. Trains rarely sell out.