buying train tickets on day of arrival

if I wait to buy after landing, the ticket will cost at least as much
(if not more) as buying a changeable ticket in advance.

In Germany, and I imagine it is the same in Italy, a changeable ticket is the highest price ticket, no matter when you buy it. You only get a cheaper ticket when you purchase a non-changeable ticket in advance, and those tickets are for a specific train (day and time). If you don't get on that specific train, the ticket is worthless.

Nice try, but no banana!

A fully flexible ticket means that you can use it on any train that day, but it will be at full price.

Where are you going? If you're using a regional train in Italy, the price is always the same. So it depends......

A changeable ticket would be a ticket at BASE price on Trenitalia. You can buy that in advance, but that price is exactly the same price you will pay when you buy the BASE price in the spot. The BASE price purchased in advance let’s say today will not be any cheaper than the base price purchased on the day you arrive. You ca of course purchase a discounted Economy or Supereconomy fare ticket for later in the afternoon, and chances are you will be able to catch in time unless there is a major flight delay or cancellation.

If you buy an economy ticket you can have it reimbursed if you purchase the option TIrimborso. However there is a 20% penalty and then if you need to change it before the time of departure departure then you would still have to purchase a BASE fare.

High speed train from Rome to Florence. Trenitalia.

So - buying changeable ticket in advance is the same cost as buying day of, correct?

In that case, why not just purchase ahead of time?

Exactly the point.

The main reason not to buy the tickets ahead of time at full price is because if you arrive much earlier or later than your train you will need to go through the process of changing that ticket to another train. This means dealing with an agent and walking through the process of getting new seats assigned on the new train in replacement of the old tickets.
Or you can just buy the next ticket that works for you on arrival.

I believe there are multiple ticket windows in Florence but I have gone through this process in Milan on a Sunday when our regionale was late and we missed our fast train transfer by about a minute. The best way I can describe the basement Milan ticket office on this day was like something from a Fellini film. Everyone conceivable person from all walks of like were queued up and frustrated and it had a very weird vibe. The service was actually pretty quick for me the agent wanted to put me on the train I wanted and the actual exchange took about 5 minutes after about a 15 minute wait, but every around the experience was weird.

So my advice is to way until you are ready to choose the train you want.

My $.02,
=Tod

Because a changeable ticket does have a limit. The base ticket is changeable BUT you have only a 90 minute window AFTER the train has left the station. So you just walk up to the window or ticket machine buy a ticket for the next time after you arrive. If your flight is delayed or cancelled then you are not worried about meeting a train. There is absolutely no reason or advantage to purchasing a basic ticket early. AND in Italy all trains except regionals require a seat reservation for that train.

You can buy a ticket at the BASE fare in advance and you can change it or have it reimbursed but…

If your flight is cancelled or badly delayed and you arrive very late (over ONE HOUR AFTER THE SCHEDULED DEPARTURE) , your money is gone forever. You cannot change a BASE fare ticket after one hour has elapsed from the time of train departure and it is NOT REIMBURSABLE AT ALL AFTER THE TIME OF DEPARTURE.

In other words, you can modify a BASE FARE ticket as many times as you like up to the time of departure.
You can modify it ONLY ONCE after the time of departure but before one hour has elapsed. After one hour from departure it is no longer modifiable.
You can have it REIMBURSED UP TO THE TIME OF DEPARTURE (not sure if there is a penalty for full reimbursement)

On Trenitalia, the Economy ticket offers a discount when purchased in advance, and can be changed prior to the departure time under these conditions - and sales channels should include the app:

Changes to booking/ticket:up to the departure of your train, changes may only be made to the date or time of departure for the same category of train or service purchased. In this case, you are required to change your ticket (at sales channels where this operation is permitted), by paying the price difference between the original ticket price and the available Base price for your selected change. The new ticket will have the same characteristics as the Base ticket.

But your strategy regarding buying a full fare ticket in advance may offer a better choice of seats if you end up on the reserved train, and making a change would incur minimal extra cost, if any:

Booking changes: permitted

Up to the departure time of the booked train: an unlimited number of times.
After the train has departed: only once, up to one hour following departure.

On Frecciarossa, Frecciargento and Frecciabianca trains, booking changes are made in relation to the Base price available at the time of the change and the new ticket will be the same price as that originally paid. If the available Base price is higher than the one originally paid, you will be required to pay the price difference for your selected change (using the Change Ticket feature at points of sale, where permitted). If the available Base price for your selected change is lower than the one originally paid, the price difference will not be refunded.

On Italo, the Economy fare also allows changes, with additional fees:

https://www.italotreno.com/en/the-train/fares

With the app, making changes is easy, and if you have wifi on your flight, you could even make changes in the air.

If you're feeling lucky, give it a try. You most likely won't encounter the worst-case scenarios cited above.

You can buy a ticket at the BASE fare in advance and you can change it
or have it reimbursed but…

If your flight is cancelled or badly delayed and you arrive very late
(over ONE HOUR AFTER THE SCHEDULED DEPARTURE) , your money is gone
forever. You cannot change a BASE fare ticket after one hour has
elapsed from the time of train departure and it is NOT REIMBURSABLE AT
ALL AFTER THE TIME OF DEPARTURE.

This is why the initial purchase would be for a train much later in the day, and fully expecting to need to change to an earlier train.

Day of arrival is a Wednesday at end of March. If we wait to buy until we land, is there any chance that we wouldn't be able to get tickets? If the plan arrives on time, we're talking late morning/early afternoon.