Online only banks offer great rates on savings accounts. The Fed has an influence but these rates are market driven. If you want high rates, look for them and put your money there. Many financial products are only available to the wealthy but in this case anyone can do this.
I think traditional banks, which apparently used to have much better rates even with all the expenses, have found that people are perfectly willing to give them their money practically for free. The newer online competeritors need something to draw in costumers.