The only reason the banks accept such a piddling sum is because they immediately sell the loan to a government-run corporation(or maybe skim the interest for a year or two).
In the 1800s before the government stepped in, you had to put 50% down, your interest rates were more like 11%, and while the loan was amortized over 30 years it ended after 5 years, so you'd have a 25-years balloon payment at the end. That's about what it would take for me to consider that loan worth it. The modern term for a loan that isn't sold to the government is a 'portfolio loan', and some smaller banks or hard money lenders will give it to you. Expect 1800s-style loan terms for an 1800s-style loan.
The only time I'd loan money out at 3.25% if I were expecting you to default, and wanted to get your 20% down payment for free when I foreclosed as the noteholder.
[1] Okay, I might actually take it in that case. But not because it's a good deal on paper.
Being ignorant of the situation, I went to fact check this statement and was blown away by how true it is. I'm flabbergasted at the amount of involvement the US government has in the mortage market. More reading if anyone is interested:
1. https://www.frbatlanta.org/banking/publications/financial-up... (Somewhat outdated but mostly good info)
2. http://blogs.reuters.com/bethany-mclean/2013/08/20/getting-g...
3. http://www.npr.org/2015/03/24/395119065/as-economy-rebounds-...
4. http://www.npr.org/sections/money/2015/04/21/401259676/who-o...
Making a transaction more complex doesn't change the fundamentals. You either save and buy, or take a loan out and buy, or you don't buy. Anything else involves some form of charity.
Market dynamics are not magic. If it's not profitable to lend money, no one will.
The only way I could see rates hitting zero would be if the government started charging interest on money sitting in banks. Such an event would not be a sign of good housing opportunities so much as a sign of significant economic struggles.
Just one example.
Islamic banks do not provide interest free money. They just use a variety of different legal structures so that there isn't anything explicitly called interest in the agreements. Usually involving the bank buying the asset and selling back to the borrower at an inflated price.
Islamic banks still profit from loans.
http://finance.yahoo.com/news/30-fixed-mortgage-rates-fall-1...
And this is not theoretical, the usual way to get a mortgage around here is Euribor with a margin for the bank added, practically no-one gets decades-long fixed mortgages.