In reality just paying the rent of 40M people is cheaper than anything else, assuming you care about society. Assuming a national average of $1000 per month rent, that's $40B a month, which is chump change compared to what the Fed is printing. Or, you can kick all these people out on the street, and give the money to the banks directly.
Of course its 40M people being evicted, not 40M apartments. So these numbers will be closer to $10B a month.
Imagine a retired teacher who decides to rent out a garage apartment to supplement her pension - is she taking advantage of 'inflated rents' if the rent amount barely covers a proportional amount of the mortgage?
Additionally, landlords have to pay 'inflated property taxes', 'inflated utilities', and 'inflated garbage service' - these aren't discretionary costs for a property owner unless you advocate letting people stay in their apartments, but without landlord contributions to water, heat, cooling, garbage.
As far as explicit coercion I really doubt that and I doubt it would be even necessary. For many, many reasons politicians are heavily incentivized to just flood the system.