So why change it in the direction you propose? We're back at my initial complaint: This turns into "Saving money rather than spending it deprives us of the tax we would have received, so we'll tax your saving as if you had spent it. Don't own a cell phone? Pay us the taxes that would have been on your monthly bill anyway. Don't own a car? Pay us the registration fee anyway. Walk to work? Pay us the gasoline tax anyway. Don't drink alcohol? Pay us the taxes as if you did. Don't smoke? Pay us the taxes on the cigarettes that you could have smoked. Don't visit national parks? Pay us the entry fees anyway."
Do you see that that's insane? But if it's insane, why isn't "imputed rent" as something taxable insane?
Politicians have been using that method of accounting for years, when describing taxpayer savings.
And it's not quite the same, but the method of tabulating the number of deaths in Puerto Rico after Maria also comes to mind. No "receipts", just statistics of what the numbers should be.
If you had to pay taxes on the imputed $4k a month then you would prefer to rent it out to someone who actually values it at $4k a month, and move yourself to a house that is better suited to you.