Except that, as a business asset, the property can be depreciated to produce income. The depreciation is based on the purchase price. People might quibble that the income you get is non-cash, which is true, but it is income.
"Sunk cost" is not a well defined term so I think that is why it is debatable. In most cases if something is a sunk cost then that means it is ignored for making decisions now. In this case, however, the extra depreciation must be considered to make a sound decision and that does depend on the price paid.
I agree with you that the number (purchase price) matters, insofar as various tax calculations and whatnot use that number has an input. However the cost does not matter directly when making a decision to sell an asset or keep it and hope the price goes up. It only indirectly affects the decision in that it affects the outputs of those calculations, and said outputs are inputs into the decision.
I think we are saying roughly the same thing. If you have a rental property you paid $295000 for 3 years ago that is worth $200,000 now then the analysis goes something like this:
Keep it option: Your income is rent+$10,000 in depreciation. Your expenses are PITI+rental expenses. Based on the assumption that rent=PITI+rental expenses this option produces an income of $10,000 a year.
Sell it option: You get nothing, assuming you can sell it for the mortgage balance. You can't take a capital loss because it is a personal residence
Of course there are other things that come into play, and teh purchase price is somewhat like a sunk cost.
A better solution might be to keep it long enough to legally convert it to a business property so that you can take the capital loss.