I get new quotes on my household insurance, flood insurance and car insurance every year. If I find a lower price and they are willing to waive agency fees (just ask, they often do this) I switch and notify my bank escrow account manager of the new policy and vendor. This has saved me over $1000/year in escrow set-aside money that is added to my monthly payment.
I then use that extra money to pay down the principal on the loan which further lowers my payments, because the loan has the same number of payments to run but less principal owed. Check it out!