Banks today are large fiscal intermediaries. They originate most of the mortgages today but own very few of them. Buying the banks won't provide access to "cancelling mortgage debt" but simply access to originating mortgage loans.
If the government called for banks to repay their bonds to the Federal government, the credit markets would dry up and businesses would begin to collapse as banks cancelled their credit facilities. and they were forced to liquidate.
Banks don't do long term lending today, so buying the banks won't give you access to many mortgage loans, mostly short-term adjustable-rate balloon instruments.
As an aside are you planning on buying all the foreign banks doing business in the country as well as all the non-bank banks and other lending entities.
So, assuming your primary goal is to cancel mortgage debt without creating worldwide depression, the government would have to "print" trillions of dollars (create debt instruments) and use those dollars to purchase mortgage loans from the various institutions that hold long term debt like pension plans, foreign governments, insurance companies, etc.
Buying back all the mortgages if it could be done would put $11 trillion of capital back on the market looking for a new home that would create asset bubbles in a host of other areas.
The one thing I don't disagree with you over is that easy credit combined with easy monetary policy (the two are linked) does contribute to asset bubbles and or minimally asset inflation. But the solution you propose of buying banks won't fix that and it seem pretty unfair to reward people with the biggest mortgages for having them. I say that as someone that loaded up on mortgages last year, when the rates were under 3.5%.
But again, housing prices are less a function of mortgage rates and more a function of land availability and material cost. If you need 3 million homes to be built to "house" people, those homes have to be built at no less than the cost of the land and materials that go into them. Already built homes then have to be priced against the ability to buy a new home or people will all buy new homes.
Only when there are no new homes available does "competition" bid up the price of homes above their replacement cost. In the end, seems to be what bothers you most... the premium homes go for over their cost when the supply is constrained.