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I simplified it more with the frozen price and wage scenario so there would be less factors to consider. Having prices and wages frozen doesn't make either option more or less favorable, it just simplifies the example.
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The problem with your made up scenario is that market prices would change to reflect a change this drastic in the market as you're eliminating one of real estates strong points.
Considering the estimated inflation rate at the time would be built into the intrest rate of any loan you had out I'd say it pretty hard to separate from the issue.
Real estate bought with debt is a double inflationary hedge, becasue the real estate holds it's value against inflation and the loan is paid off in 'cheaper' money. Since it's considered a hedge against inflation the precieved value of real estate changes relative to inflation rates in the market.
If you don't think this would drastically alter real estate valuations look back at average real estate appreciation rates when we were on the kenshin or true gold standards and had no inflation. Seriously you can't just change the rules of the market that drastically and then pretend that the market wouldn't reflect said changes in its pricing.
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In any event EVEN if we look purely at your example; individual rentors get a rentors credit. Owners pay property tax. Owners have to do standard upkeep and maintenence on a home, as well as do major overhauls periodically to offset depreciation. Owners are liable for any damage cause to the property via 'act of god' type incidents normal maintence aside. Now figure in the closing costs on the transaction.
How much money do you think rentors save per year when you start figuring all these factors into the mix. Now lets assume a rentor took the difference and invested it over time in an appreciating asset since in your magical faery-tale the house isn't appreciating.