This is the common misconception....the money doesn't come from the Gov't to the Fed. The Fed prints the money, any sienorage (earnings) it earns on the money it prints and lends is paid back to the Treasury. Also, when the Fed prints new money it either lends to the financial institutions via the discount window or it buys Treasuries directly from the government (i.e. the Fed gives money to the Gov't).
When the Fed lent money to the banks via the discount window, they did that to shore up the capital bases of the various financial institutions. The Treasury never paid for it....matter of fact, the argument can be made that if inflation runs away like doomsayers have been predicting since QE1, the Treasury will benefit - because inflation is simply a tax on the poor.
But, inflation has been subdued, despite constant harranging from doomsayers, and growth has been tepid. The Fed took on over $2T onto it's balance sheet because it is the only organization in the world that can. It wasn't up from $500M, it was up from $500B. You were off by only a factor of 1,000. So it only swelled 4X....considering that the price of not doing that would have been a great depression that made the depression of the 40s look like a mild recession, I would say it's worth every penny.
Also, the reason public debt has expanded is because of the borrowing the government has had to do to finance things like increased unemployment insurance, increased medicare/medicaid claims and tax cuts for everybody.
Also, because interest rates have been at all-time lows...i.e. most investors still see US Treasuries as the safest asset around (comparatively speaking).