Or not so stupid.
They do it because it works.
Most people don't keep a close eye on savings. They pick what seems to be the "best" account, plonk their money it is and forget about it until they need it. They don't regularly check rates, let alone comparative rates.
Banks compete with each other, and rates is the main tool to do it. They get new customers in, usually away from other banks, by aggressive rate-led marketing, but they have to keep doing it, because the opposition sure are. So they offer attractive recruiting rates, but then .....
They rely on customer apathy and inertia. It's a pain to keep opening new accounts in order to move your money, and most people won't do it. And the banks accept that there are those that do do it, and that they lose those customers, as inevitable collateral damage and of far less importance than attracting new business. They'll cheerfully sacrifice 10 savvy customers to gain 100 naive ones.
A smart saver is aware of all that, and if you want to maximise income, play the game. Keep an eye on rates, and move it about. When you move away from an account, don't close it. Keep a modest amount in it and every once in a while, do a deposit and removal or two. Or, if you have online access, bounce an automated payment around a bit. Banks have a habit of just closing inactive accounts (and sending a cheque for the balance). I've had it happen to me when I took my eye off the ball.
But if you keep the account open and modestly active, it's much simpler to open a new account when a bank you're already known to becomes top of the tree again.
Of course, whether it's worth playing the game entirely depends on how much you have in savings of this type.