By the real interest rate I mean the interest rate after taking inflation into account. If you think about it, the average long term nominal interest rate in the economy is going to be roughly in line with nominal growth of GDP, because there are market mechanisms in place to make it so:
If the nominal interest rate exceeds nominal growth in GDP, then wealth effects (aka people have more money thanks to interest and therefore spend more) will eventually encourage faster growth of nominal GDP - either by stimulating more production (real GDP growth) or by driving up prices (inflation), or, more likely, by a mix of both.
If nominal interest rates are below nominal growth in GDP, then it becomes more profitable to borrow money to invest in production. People will do this, and this will adjust interest rates up (you can understand this from two directions: on the one hand, profit is being spread around via interest, on the other hand, demand for loan drives up interest rates).
These adjustments do not take over night - they probably operate on the timescale of years (unfortunately, economics tends to pay very little attention to how fast such market mechanisms operate, so we basically have no scientific basis for such statements, just common sense and gut feelings). Still, you cannot escape those adjustments of the interest rate in the long term.
What does this have to do with governments, inflation, and financing the deficit? If the government consciously acted to increase inflation to finance its deficit [1] this would indeed temporarily benefit borrowers. However, this is a temporary measure and certainly not the case today. Furthermore, governments have also consciously acted to decrease inflation, which obviously has the opposite effect. So in the end, it's at best a wash.
One last point:
the Fed does in fact purchase US Treasury Bonds without requiring the Treasury to pay back the debt
The same happens in the real economy as well. Firms operate using debt that is effectively never paid back. The debt is regularly rolled over, sure, but it is de facto permanent and contributes to a permanent increase of the money supply, which is what matters (if any of those quantities matter).
The Fed does buy mostly Treasuries to create the monetary base (which is necessary for purely technical reasons), but what else would you have them buy? I personally wouldn't want "my" central bank to gamble on risky assets.
[1] Also, I find it fascinating that the goldbugs never point to actual examples where this happened. I suspect they don't because it's a myth, at least in the countries those people come from outside of wartime.