Full size motorcycles are very common in Europe, including Italy, but I would rarely take mine on the freeway. Too boring and dangerous with cars and semis traveling at 120+ km/h. The fun of having a motorcycle is riding it on the curvy country roads.
The same is actually true in America. If you want to see hundreds of motorcycles in California, get out of the freeways and drive on a weekend along the curvy CA-35 (Skyline Blvd) on the watershed of the Santa Cruz Mountains on the San Francisco Peninsula. Then stop for a bite at Alice’s. You will see hundreds of fancy motorcycles.
Regarding your plans for a day trip from Rome to Saturnia on a day trip, I would consider it a stretch with a full size motorcycle, but with a 125cc Vespa on the same day, no way, I wouldn’t do it. A scooter can’t travel on freeways and with a 125cc Vespa, the top cruise speed you can hope for on regular roads is maybe 70km/h. Since you will have to go through towns and regular roads, maybe you can keep an overall average speed af 50km/h at best. That would mean almost 4 hours each way because Saturnia is about 160km. Just to put it into perspective I’ve taken my 125cc Vespa from Florence to Arezzo, Florence to Viareggio, Florence to Siena, Viareggio to Riomaggiore (all half the distance you intend to cover), and each time it was a “Trip” with a capital T.
I wouldn’t drive a Vespa to a day trip to anyplace farther than 80km each way. Your trip is twice that distance. If you do it, post your adventure here. I’d like to hear about it. I hope your “arse” can take it too.