tl;dr:
In a high cost of living area,
Mortgage Interest Deduction + Property Tax Deduction + Investment Gains > Mortgage Interest Paid
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In our very high cost of living area, the mortgage interest deduction is a substantial benefit, well above the standard deductions. And all itemized deductions are cumulative -- you don't get just the marginal benefit of the mortgage interest over the standard deduction, you get it all. As an example, if you have enough other itemized deductions to equal the standard deduction, then your mortgage interest is deducted fully at your tax rate, not just marginally over the standard deduction. Also, property taxes are deductible as well.
Where we live, we carry a mortgage that's ~ $420k, with additional ~$8k/year in property taxes (did I mention housing is expensive here?). I think last year those two items alone totaled somewhere around $30k in deductions. Combine that with all the other deductions (kids, charitable contributions, education, etc.) and it becomes a big deal.
Particularly at today's low interest rates, it's also a large benefit to take the money that would have gone into paying down the principal (thereby reducing the mortgage and associated interest), and instead investing that money elsewhere at a higher rate of gain. Since our mortgage interest rate is only 3.8%, with a healthy part of that deducted off of our taxes, it's a no-brainer to get a higher rate of return by keeping the mortgage and deductions, and instead investing in stocks/etc.
As others have said already, the mortgage interest deduction is not a reason in itself to buy a home, but it can be a nice benefit if you're carrying a large mortgage, particularly if you're a high earner. And I would always carry a mortgage in today's interest rate environment. Not to mention it's probably the best inflation hedge you can find, it's practically like free money.