My wife and I are flying into Rome, then plan to immediately take the train from the airport to Termini Station, then high-speed rail from Termini to Florence. I was going to pre-book our tickets from Rome to Florence, as I normally would, online or with the app. However, since we are flying in that same day, I am concerned a late flight may make us miss our train. Similarly, I don't want to plan to wait hours in the Rome airport or Termini train station "just in case" we come in a late from the US.
Do you see any reason why I can't just buy same-day business or 1st class tickets at Termini Station?