Birdman, thanks for the analysis, this should be interesting discussion...
Let's analyze the effect.
Fed purchases loans (or already has), which injects dollars into the economy.
Fed forgives the loans, meaning it never receives the dollars back with interest (which actually futher increases the NPV of the money it injected, because now the effective amount injected is the NPV of the note, not just the principal)
So the money supply stays the same or increases, but now those debts are gone, meaning a huge amount of capital is available, which increases the velocity, meaning what has been holding prices down (velocity making up for money supply increase) for many things (ie those that CPI actually measures) is instantly gone...so a huge inflationary spike occurs.
I think I am with you up to the conclusion. I think the conclusion is wrong for several reasons...
1) I don't mean all debt.
I hope y'all weren't assuming that. I don't even mean most debt.
2) Keep in mind that the total private mortgage debt of this country is approx ~$13.3T and falling fast. Compare that to the $2-4T already injected that have basically done nothing. And the 0% fed rates, which has basically done nothing.
If the fed buys up debts and forgives them, you will see a taxpayer revolt among those who lived frugally. and paid off their debts or never had any debts to begin with. Maybe there's not enough of us to matter 
3) Yes, good point. A more equitable arrangement could probably be made so that those who are debt free end up with straight cash so that moral hazard is not reduced. Perhaps a per capita cash injection, but only those who are debt free get to keep it, the rest are required to pay down debt. In one sense, it will feel a lot like a conditional tax deduction.
4) A small program could be used to slowly feed in this debt forgiveness. As soon as deflationary forces begin receding, the program could be withdrawn, and normal fed rate tools can begin to work again. Remember we are below 0 lower bound and creating trillions of new cash, and it has done NOTHING. Its hard to say at this point how much leverage this program would have. On one hand it would inject cash directly into the consumers and lenders and stop deflation in its tracks; on the other hand it would destroy money supply as debt is forgiven much like a bankruptcy process. As I said, the program would need to start small and cautiously as it slowly drains the debt out of the system.
My reasonings depends on some unspoken axioms though:
DEBT is the major problem this country and most of the world faces. Currently we are unwinding that debt, whether by paying it down or writing it down (bankruptcy). Fortunately, despite the low interest rates, people in aggregate are not taking on new debt - and that is a good thing. We have a lot of debt to unwind first.
The velocity of money through the system is too low, and needs to be increased so that we are all productive in the right fields to help rebuild real wealth, not ponzi asset bubbles.
The reduction of debt load slows down this velocity and causes deflation. I tried to reason through in the previous post why this seems to be empirically true. This seems to be empirically true whether I have the exact system flow right or not.
Increase interest rates...which they can't because of it would require increasing Rate's on treasuries to maintain even the small (compared to the fed) non-fed purchases of treasuries in the cycle. An interest rate rise sufficient to cool the velocity you just reacted would be a rise to probably "classical" 5-7% rates, meaning national debt interest would spike to close to a trillion a year...which the govt can't affor, and would have to deficit finance through treasuries, which the fed would have to purchase to maintain demand, which INCREASES money supply.
I think I've already answered this above, but also add specifically that it is NOT the FedRes's job to keep the Federal gov't solvent. That is a whole 'nother ball of wax. It is the FEDRES job to keep inflation between 2-5% and unemployment at <4%. And when I consider that the national problem is debt, I fail to see why letting the federal gov't create another debt bubble is the right solution. Switching from a private debt bubble to public debt bubble doesn't solve the axiomatic issue: too much debt. [Modern Keynsians, like Bernanke and Paul Krugman, fail to see this because they don't think debt matters. I think debt does matter to the behavior of the economy.] If the federal gov't is in so much debt that it can't pay the interest in a regular inflationary environment, then the gov't needs to be cut back severely.
you likely created a situation where potential purchases wouldn't purchase that debt, because who know what the fed will make worthless again.
Can you clarify this sentence? I wanna make sure I got your meaning before responding specifically to it.
What needs to happen is a pullback (sell the assets it does have) AND let people/businesses/etc default...which will remove dollars, and reprice assets to keep things moving.
Welcome to the nightmare of the 1930s. I'll just reiterate, we need to drain the economy of debt and prevent deflation to help us correct the fundamental problem. And masochism is not a virtue.
