You're right: my feet no longer touch the ground any more, and I hover majestically above the steps like some kind of evil spirit. However, no carpet could withstand the sheer tonnage of carers I have traipsing up and down every single day – if you can imagine a herd of wildebeest wearing spiked running shoes, that should give you some idea.
I would always advise going for a model with battery backup, because even if power cuts are rare in your area, if you've become more dependent on the lift and there is a cut, it is GUARANTEED to come at the most awkward time.
I've always felt completely secure on mine, and there is a seatbelt if you need it. Also, you usually get options on positioning and style of control buttons: by sheer luck I went for a joystick on the left arm, so I can still operate it with my wrist. In any case, there are buttons top and bottom so that other people can work it, and there are safety bumpers all around which immediately cut the power if anything becomes trapped while moving.
Bob, I think I've seen other stair climbing models which have a strange, three wheels in a triangle kind of arrangement. They're expensive, though not as much as the Segway, but I can't imagine how terrifying they must be to use!