Welcome My Brother. You want a logical answer so I would like to give you a logical answer.
The Black Stone Is not an idol. We are not worshipping the black stone but we are facing it for worshipping God. The logic behind this is Unity.
People from anywhere when face the same point, there is a sense of unity between them. Look at the below rough diagram:
When Muslims from all over the world face Kaaba, they become united unconsciously.
To Worship God we have to pray and for praying we will face at some direction. If there was no Kaaba, we would be unable to identify direction. One would pray to South and the other to North. One to west and the other to East. So this would produce confusion and inconvenience for the community.
Tawaf Around Kaaba Have you looked at model of atom where electrons revolve around Nucleus.
Why do they revolve? Because this provide atom with stability and strength. When people from different sectors of the planet revolve around the Kaaba, this produces stability and strength in the community.
At Last There are no answers for some questions. If Muslims had no kaaba, these people would say "Hey Look! They even don't have a specified location for their worshipping. One is facing there and the other is there!" If we faced South, they would say "Why are you facing south? Are you worshipping South?" Same problem would be for any direction.
Disclaimer My answers here are logical, so should not be criticized for not having reference or that this answer is not Islamic point of view.