To be clear, the password can be checked at login-time, rather than registration-time, at which point the service should send the user through an account recovery process. There's still scope for passwords not appearing in the HIBP dataset, but it's massively reduced.
Do you mean this link: https://news.ycombinator.com/item?id=39116531 ? I'm not sure I agree with your conclusion. You should be able to successfully highlight a unique IP address making ~4,400 discrete login attempts across a month as suspicious - and further highlight that there are 1,000 other IP addresses behaving in the same way. Most users login from a handfull of predictable IP addresses, and most IP addresses login with only a couple of predictable accounts.
These types of login analytics aren't beyond the ken of man, and a service like 23-and-me should definitely not be able to allow 4.4m attempts and 14k successes from a small set of IP addresses without it raising some internal alerts.