But would the banks have all originated subprime loans had they not been able to repackage them and sell them? By selling the loans they were kept off the bank's balance sheet.

If the Fed is buying up all kinds of bonds and the banks know this, there's nothing preventing them from selling their older bonds which were purchased at a time when interest rates were higher (and thus bond prices were lower) and selling them at a profit to the Fed. They then need to do something with the money, why not buy some new bonds?

Just because the Fed isn't participating in the primary auction doesn't mean that they're not influencing the Treasury market in a huge way.