If your analysis is correct, then the only honest thing the CEO could do would be to shut the service down. And that obviously isn't going to happen: no one shu

If your analysis is correct, then the only honest thing the CEO could do would be to shut the service down. And that obviously isn't going to happen: no one shutters a profitable company over the trivial inconvenience that its core product doesn't work, and the actual stakeholders have obvious incentives to convince themselves that it DOES work. If you are unwilling to sell something useless, then your best bet unfortunately is to quit.