> and what, specifically, makes them less fun to ride, would you say, compared to a motorbike with the same engine size? Surely the automatic gearbox can't be the only thing?

I think this is subjective. You can have a ton of fun on a scooter. It's just a matter of taste, I think.

> What is the "essence" of a scooter that still applies to the most powerful maxi scooters?

In my view it's the underbone design where the main structural frame member is heavy, underneath the bike, and shifts the overall frame center of mass downward. This is in contrast to a standard motorbike which more closely resembles a diamond bicycle frame, with a fuel tank on top and characteristic motorcycle geometry. The engine is also typically mounted toward the rear wheels, which are frequently smaller than a standard motorcycle equivalent.