Before June 2013, FHA mortgage insurance had a cancellation feature. If you put 10% or more down, your annual MIP dropped off after 5 years and the loan reached 78% LTV. If you put less than 10% down, you still had a path to MIP cancellation through the original schedule.
HUD changed the rules in June 2013. Loans originated after that date have MIP for the life of the loan if down payment was less than 10%. Even with 10%+ down, MIP runs 11 years before dropping.
Here's the problem: if you streamline a pre-2013 FHA loan, your new loan is governed by post-2013 rules. You give up the old MIP-cancellation feature. Forever. The new loan will charge MIP for 30 years.
Some borrowers should still streamline anyway — if the rate reduction is large enough, the lifetime savings outweigh the lost MIP cancellation. Many shouldn't. If you're 6 years into a pre-2013 FHA loan with a rate that's only 0.5% above current, you may be better off either paying down to 78% LTV and dropping MIP — or refinancing into a conventional loan once you have 20% equity, which has no MI at all.
A streamline officer who doesn't run this comparison for you is doing you a disservice. Always ask: "what was my original MIP cancellation date, and what does my total MI cost look like over 10 years if I streamline vs. if I don't?"