Yes. That's why both houses cost the same.
The interval technique makes sense to me on goods that are used over time or taxed over time. You can pay for a house all at once, and if you were only paying property tax once I think I would agree with you that the tax is consumption tax. Yet property taxes are annual, so in order for property tax to be a consumption tax we would have to enumerate how much consumption is occurring during that year.
Consider something simpler, like a sofa. We both buy the same sofa with a service life of 10 years. Did we consume the sofa when we bought it? Or do we consume it over its useful life? If I jump on the sofa daily and it lasts for 1 year, I've consumed it in a year. If you barely sit on it and it lasts you 20 years, you've consumed it over 20 years.
Does that make sense? How are you defining consumption?
So while it may not be a satisfying answer, in my experience, self-circular is just sort of the way it is.
Also, the consumed / depreciated value comparison doesn't sit right with me, since for business expenses (tax write-off purposes), it's based on zero value at end of life. Any previously depreciated value recovered at sale has to be (re)taxed; you only get to ultimately deduct true depreciated value, albeit (re-)payment is delayed to year of sale.
Regardless, real property (non-movable) is rarely disposed of for zero value, so "depreciated" value isn't a good estimate for "consumed " value.
Is one year of your consumption equivalent to one year of my consumption? Like a car, the longer you use it the higher the likelihood that something expensive goes wrong. But unlike a car, our homes are probably appreciating at close to the same rate.