I believe that in most jurisdictions, the "guts" of property tax millage formulas is based on a 10-year interval (or maybe more accurately, 1/10 of the assessed value). However, that's always seemed arbitrary to me, as: 1) it's never "paid-off" and 2) millage rates are set in conjunction with this known value.
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.