Closing costs can be rolled into and included in your mortgage but if you do roll the closing costs into the mortgage then the closing costs will cost more due to the interest that is charged on the closing costs during the life of your mortgage which can be from 15 to 30 years depending on the length of your mortgage.
That interest just for the closing costs can add up over those years.
Interest alone on the mortgage will add up to a substantial amount so you'll be paying around $100,000.00 in interest on a $250,000.00 home.
So if you can pay off the mortgage faster by paying extra payments towards the mortgage you'll save a lot of money on the mortgage in interest.