> Is it to protect the vaccinated? This makes no sense, as the risk to the vaccinated well below the range we have accepted for decades.

What is the acceptable range? Older people are still dying from Covid even after 2 shots. If a third shot can improve someone's protection from death due to Covid, say from 70% to 90% [1], that sounds like a good reason to take that shot.

The comparison between someone in Israel taking a booster shot and someone in a 3rd world country without access to vaccines is irrelevant - at least until there's a serious global initiative to provide vaccines to everyone around the world.

[1] Original stats talked about 90% protection, but that has gone down since then. One of the possible reasons is the need for a booster shot. But we still don't know what level of protection the booster shot will provide.