You make a lot of good logical points, but religion isn't logical.

You can read up on Abrahamic Religions below

https://en.wikipedia.org/wiki/Abrahamic_religions

The gist is that all these religions have a common ancestor with some slight differences. Jews are still waiting for their savior, they recognize Jesus along with the Muslims as a prophet, but not their savior. Muslims recognize Mohammed as the final prophet, but not a savior in the sense Jesus is to the Christians.

Trust me, they have thought about it and all agree they worship the same god even if they have different key prophets (Moses, Jesus, and Mohammed). It is weird and confusing for sure.