Bags rarely get really totally lost, but they do get temporarily mislayed, and I would rather be staying in the city whose airport I am flying into rather than in a city a long train ride away. My bag had never been mislayed in many decades of travel until this past year when it went astray twice --- both times it was lost in my home airport (no idea why!), so it wasn't a big deal and I got it back.
Florence is a nice small airport and close to the historic center --- after a long flight and because I am very familiar with Florence's big busy train station, I'd probably want to take a taxi from the airport to my accommodation. Especially with four people, a taxi makes sense.
Also, assuming jetlag, I'd rather transfer from one plane to another in Munich without luggage to deal with, than to have to collect my bags, train into Rome, get another train to Florence (dealing with my bag the whole time), and walk from the train station to hotel or apartment. It is of course possible and we have done it several times in Italy, but really not what I would call fun. Although if you can pack as lightly as, say, Jean from Idaho, that would make a difference.