They are actually pedaling and moving, but they need less strength and stamina to get further. They dont end up stuck downhill unable to climb up. This latter risk is something that really forces old people to put out of normal bikes. For older person, the e-bike is roughly the exercise they need. And it gets you to places, it does not limit them to small area.

The old person alternative to e-bike is not normal bike, it is nothing, because their bodies are just like that - weak and old.

I think the health benefits would be the ability to get out and be involved with the world. When I was living in Chinatown I was amazed by how much healthier the elderly people were simply from going to the park each day and hanging out with their friends or dancing (Chinese people, at least in the US, seem to LOVE ballroom dancing!). The problem is that not everyone can live in a strong community where they can walk to a local park.