The only stupid thing to do would be to pay off a 2.8% mortgage. Opportunities to safely earn more than 4% are everywhere in today's environment, even in treasuries or CD's.
I too have noticed the 6+% yields on annuities and thought about the mortgage arbitrage opportunities. For example, instead of paying cash for a house, get a mortgage and buy an annuity to pay the mortgage. When the house is eventually paid off, the annuity becomes an income source for the rest of your life. That's a better deal than merely tying up one's money in a paid-off house.
This strategy might make the most sense with a 15 year mortgage, and especially for a young person. 15 year rates are around 5% now, so depending on age one might make an immediate monthly profit by using an annuity this way.
We're kinda in a strange spot with interest rates right now. Somehow, many corporate bonds are yielding less than comparable-duration treasuries, particularly for AAA and AA companies and durations less than 7 years. Meanwhile, those 6%ish returns advertised on immediateannuities look completely out of line with the returns on other assets, like the 4% yield on 20 year treasuries for example. So I'm kinda skeptical those rates are real (don't believe everything you see on the internet!). Dropped a line to my insurance agent to find out.
