This "common vespa" as per this photo, is not common at all in Greece.. Not in the way that is shown on that photo..
People do use motorbikes and scooters because the waether permits it.

I have worked and spent whole summers on island like Mykonos, and Santorini, and i have seen decades of accidents happening, some ending badly. For that reason alone i would discourage anyone wanting to rent a scooter.

Clausar, the plural of 'anecdote' is not 'data'. Please provide a link to any statistical data you can find that bears out your contention that it is not common in Greece.

I have seen many instances of the 'family Vespa' in Greece and in many other countries around the world. My anecdotal evidence is equal to your anecdotal evidence which means neither can claim any empirical evidence to support either contention unless you or I can come up with data to support that anecdotal evidence.

At times in my life I have ridden a Vespa (including on Greek islands) for years as an alternative to a car. I would not hesitate to ride one on Santorini.

That is my 'fact'. Your 'fact' is you would not ride one. I wrote, "On an island the size of Santorini, I wouldn't even think about renting a car. But YOU have to decide for yourself."

I gave my opinion but left the decision up to the OP, I suggest you do the same.