While I agree with your assessment of the need for social security being brought on by mortgages, I disagree that we would be better off by not havinga mortgage.
If one chooses to rent a house instead of buying, the end result is that they have paid nearly the same amount of money in rent as they would have in paying a mortgage. The only difference is that at the end of the 30 years the owner has something of value and the renter has paid for a house that the landlord owns.
The real need of social security is created by its very existence. If social security did not exist and had never existed, then people would not rely on it and would plan for their own retirement by investing and saving.