Right now any person in the world can contribute to Wikipedia because of their notable sources policy. Any person in the world can validate and correct mistakes.
Would homeless people write their own biography? Noone will be able to verify this information. How in the world this improves credibility?
But its usability would go down. How many people named Smith, Li or Gonzales are out there? Good luck finding the right one if the count of entries go into hundreds of thousands.
Also, why limit yourself to living people only? And once you add, say, everybody whose name has been recorded in writing, you are probably looking at 15 billion or so.
Gender issues aside, Wikipedia could give a biography page to every homeless person and their credibility would only improve.