Even though I am not a supporter of MQM or want to be called Mohajir I would like to respond - but I belong to the group you are addressing here.
I believe you are getting too technical with not much effect. Contrary to what you would you like to believe the reality is that Pakistanis are mired in all sort of identities based on ethnicity, language, tribes, biradaries, etc etc. The people who migrated to Pakistan at the time of Partition largely didn't belong to a contiguous group. They were from different parts of regions now part of India and other than the language they didn't have anything common. They didn't pick this term to be identified - if you do some research on this topic you would find that the documents are replete with this term being used for people who made that decision to adopt a new country. Largely due to differentiate themselves from the tribal and ethnically focused indigenous peoples of Pakistan. Since there were no other terms to identify this large group of people except for some derogatory ones used by the locals the term mohajir stuck. Its not a very technical term but whatever was available and used at the time was carried on by people.
Have you seen those confession of target killers - did you notice the interrogator insistently asking question about the "zaat" - its the norm to use a term to identify as is the norm. If you go to any place in Pakistan you will asked where are you from - people want to know whether you are a punjabi/sindhi/baloch/pathan/seraiki/urdu-speaking and once they establish the larger association they try to pry into more specifics based on region/tribes/biradaree etc.
As with any people adversity brings them closer and sometime unite under a term or arrangement even if they belong to disparate backgrounds and communities as is the case with urdu speaking population of urban sindh. No one is planning to go anywhere - I am sure many will be disappointed but we are a reality and are here to stay ;-)