The "Kingdom of God" does not literally destroy world governments in the future any more than it did in Jesus' day.
The "Kingdom of God" is an ideology. The man does not enter the Kingdom until first the Kingdom enters the man.
Jesus taught us to pray "Let your Kingdom come". Express willingness to allow that Kingdom to enter your soul. "Let it come to me".
If the subjects of any kingdom do not first believe IN the kingdom, then that kingdom cannot exist. Any rulership must be willingly accepted. This is primary. The ideology must be part of you.
If people fail to accept the ideological principles of any government, then that government fails. It is "crushed". Non-confidence.
Goverments do not destroy anything. People who believe in Goverments destroy.
Armageddon is not caused by the Kingdom of God. These governments are destroyed in the hearts of man beforehand.
It is the Finger of God that destroys at Armageddon.
The "Kingdom of God" did not destroy Jerusalem in 70ce. It was the Kingdom of Rome that did that. The Kingdom of God destroyed the rulership of the false religious leaders of the Jews prior to the Roman's work.
Jesus said, as he hung on the timber, "Take courage, I have conquered the world".
But Jerusalem still stood.