If they pay banks more for reserves held at the Fed then surely the banks can then lower the rates they charge their customers?
Not really, banks can deposit reserves at the Fed and earn 0.5% interest, or they can loan to consumers and corporations. In order to make the loans worthwhile (risk of default), banks would charge a higher rate than the Fed's rate (risk free). This is a simplistic explanation, bank cashflow is a factor too, but I hope you get the idea.