Your lender is not supposed to keep too much in the account....once there is an overage past the legal limit you will be issued an escrow refund. Just like if there is not enough after distribution you will get a notice of an escrow shortfall. The mortgage company, in the event of a shortfall, will pay the taxes and insurance and adjust your monthly payment to cover the expense.
Your insurance seems high. Look at adjusting your deductible to drop your premium. I carry a 2500.00 deductible and it reduced my premium by 50%. Do the math and see if it is worth it.