I must be doing it wrong. We bought a house in AZ with a 15 year, 2.99% interest rate. The MITC made almost no difference, even for the first year where I was paying mostly interest.
You get back roughly 30% of your paid mortgage interest. But yes, you should have taken a 30 year fixed if you wanted a larger credit. Its free leverage.
You'd need to have enough deductions to itemize without the mortgage interest deduction and be making well over six figures for that to be the case. I personally don't come close to itemizing without mortgage interest, so I was seeing far less than that. My wife and I combined were barely in the six figures (taxable) when we actually owned our house as well, so we got back about $1k in taxes on about $12k in interest.
Paying more in interest in order to get more back on your taxes is a losing proposition.
Not just more in interest, you're also reducing principal so there's some opportunity cost from an investment perspective.
Really comes down to how long you intend to stay in the home.