The difference between renting and owning is income, savings rate, and lifestyle. If you can't afford to buy, you either don't make enough or don't save enough. It's the down payment that separates a lot of renters and buyers. If you are arguing homes are expensive, I'd argue that $15 minimum wage isn't helping.
Mortgage interest deductions may be bad policy, but it doesn't "tax renting." That's asinine.
That those other buyers are willing to pay a higher price affects the comparable sales, the appraisal, the "Zestimate [haha]", the willingness of the seller to select your offer, etc.
Then, assuming you did have a mortgage and qualified for the deduction (most people with one home do), you paid less (net) for the loan than you would have otherwise.
A quick google search doesn't produce results that suggest that removing the deduction would reduce housing prices to the point that people in this thread are saying. Here is just one example that states it would reduce prices by 0.3%: http://www.taxpolicycenter.org/taxvox/what-changes-mortgage-...
Reading two sentences further from that same article you linked: "completely eliminating the mortgage interest and property tax deduction—a drastic change that probably would only happen if accompanied by a new tax preference for housing—would cause housing prices to fall by an average of 11.8 percent in the 23 cities studied. Estimated price declines would range from 10.3 percent in Seattle to 13.8 percent in Milwaukee."
I'm not using the tax deduction as a "strategy for paying my mortgage". I did figure the savings from the tax deduction in modeling my budget, the effective cost of housing, all of which influenced my bid(s).
I'll try a different tactic for the explanation: What effect do you think the mortgage deduction has? Does it increase your disposable income?
Also, if a self-employed business traveler knows one can deduct the cost of hotel, flight, and meals (partially) spent during a business trip from income for calculating income tax, does that affect how much that traveller is willing to pay versus similar categories while not traveling for work?