In these trying times of rising interest rates leading to increasing burden on your finances, you may be well, thinking seriously about this option. But, it is advised not to do so.
Most banks are trying to be loyal to their existing home loan borrowers or any loan for that matter, so that they can retain their customer base.
However, apart from that fact, you need to realize that, there are a lot of hidden charges involved when you shift your loan from one bank to the other, no matter how low the interest rates are offered to you. The costs, which you will eventually bear, will be the prepayment charges ranging from 0.75% to 1.5% such as, valuation of the property, which will involve additional fees; cost of stamp paper, which differs from state to state; the cost of equitable or legal mortgage as may be stipulated by the lender; legal expenses and processing fees etc.
Summing these expenses, will give it quite an expenditure, which can be avoided.