The current government set caps on the percentage of closing costs to loan amount. There are fixed costs like appraisal and title work that do not change with the cost of the loan so at some point you reach a minimum loan amounnt with a lender. This was done to protect people looking for a loan from predatory fees but has really messed up the small buyer looking to get started in home ownership.
Some banks will and credit unions as well. A broker cannot because of anti-predatory lending laws that put a cap on the "percentage" that can be charged which makes it not only unprofitable, but at times impossible to include all the necessary fees in the cap. A 40K mortgage with a 5% cap only leaves $2000 for all closing costs and that's just not possible in most cases.