http://library.ahima.org/xpedio/groups/public/documents/ahima/bok1_049016.hcsp?dDocName=bok1_049016
1)So that the IRS can verify you have health insurance. Technically, this could be done directly from healthcare.gov, but the insurance companies need to report the people who buy insurance off exchange anyway so why duplicate effort.
2)At least in the past few years insurance premiums have been tax deductible for the self-employed, so I imagine the insurance companies report this to the IRS. I am not 100 percent sure this is done, though.
3)Another one I am not 100 percent sure on. The IRS may verify medical expenses paid through an HSA. Having out of pocket totals from the insurance companies may help with this. They may also verify the medical expense tax deduction.
SSN as identifiers are bad in the case of: non-citizens, babies, and fraud (may have multiple people with the same ID).
However, if you are dealing with government services (especially anything that touches on taxes or benefits) you'll probably need to provide a valid SSN. And then also be prepared to deal with oddball cases too.