That's not quite accurate. You average account age for
credit lines affects your credit score. Banks do not report depository accounts to the credit bureaus because they are not lines of credit, they are liabilities.
They do report to a separate group of risk-scoring companies, but this is mostly to gate fraudsters. Frequently switching checking/savings accounts will have no bearing on your ability to make large purchases on credit. If you happen to close credit cards frequently enough, regardless of whether they are issued by banks, your score could be impacted by reducing your average account age.