One reason to keep a train trip more flexible than a flight is simply because you can. For much of Italy, we're talking about trains that depart at least hourly and hardly ever fill up. Most tourists in Italy take relatively short rides that cost $5-50 at full fare, so the savings don't approach what you could save by booking ahead for other trains like Munich-Berlin or London-Edinburgh, which can cost $150 or 200, respectively.
In countries where most trains don't require seat reservations, such as Britain, Germany, Switzerland, and others, a rail pass can be very flexible to use, hopping on any train you like over a certain number of days, and that convenience can outweigh cost savings. That's not the case on faster trains in Italy, France, Spain, and some others.
Of course, you can also vary the timing of train ticket purchases. If you have a longer ride that really works best for you at a particular time, maybe you book that ticket ahead for a discount, and not some others. We don't recommend booking ahead if you're catching a train right after a flight and there's no benefit to buying regional train tickets ahead (there are addition limitations if you buy these online for Italy).
