You guys are all pretty much correct. This is by no means a hack for the sophisticated, but it's something that I think can benefit a lot of people.
Answering Q's
Yes, I had a 30-year mortgage, so paid down hardly anything in that time. About $500 of each payment paid down the principle. One month I did make a double payment because I'd had an exceptional month with my second job, so when I refinanced, I think I owed about $298,000. With the 15-year loan, about $1,500 pays down the principle.
Yes, I paid plenty of money in interest, insurance, flood insurance (always get flood insurance; I cannot recommend this enough), and property taxes, the last of these were significantly reduced because my wife and I are both disabled veterans. This is among the many reasons that people like JL Collins and Kristy Shen will say that buying a house can be pretty dumb.
I think the prime rate on the 30-year was a little under 4%, but I don't recall. I just remember what I opted for to get the closing costs to something like $6,000. When I refinanced, I did the opposite.
My Main Point
If you're like me and want to buy a home in a HCOL area, and know that the 15-year is better, and that the 30-year stinks, but have to do the lesser of these things to get in the door, it's much easier to get the 15-year when you're in the house.
I liken it to a relative of mine who couldn't afford to buy a home when pretty much anyone was getting a mortgage, so he got two loans, then had some dudes move in with him. It was not the best financial decision, but it worked for him, and will likely work for others.