Karachi belongs to all Pakistanis

You obviously don't know the history of Karachi. Karachi was a major port and economic center long before and any 'muhajirs' arrived. That was the main reason mohajirs went there.

Karachi is in Sindh, and always has been.

To say it belongs to muahjirs is like saying Bradford, England belongs to the desis who are the majority in that city.