Hi Gonzo, and thank you for your question.
If you have an FHA loan originated before reforms instituted in 2013, you do get to drop your MIP coverage once your loan-to-value ratio reaches 78 percent. MIP is not actually for your benefit -- it's to reimburse the lender if you default on your loan. So you are not giving up any benefits by dropping this monthly payment. You do retain the benefits of FHA, and the best of those is the fact that it's assumable. If rates go much higher and you want to sell your home, the ability to let your buyer assume your FHA loan at a lower-than-market rate is worth something -- a higher home price, a faster sale, or both.
If your FHA loan was closed after June 2013, you don't get to drop your MIP no matter how low you pay down your mortgage. In that case, if you can get a better mortgage rate, I recommend refinancing. Because even if you get stuck with some private mortgage insurance with the new loan, it WILL go away once your loan-to-value drops below 78 percent. You may also be able to request in writing that it be dropped once your LTV hits 80 percent.
Good luck and thank you for writing.