> How long do you sit in a bath?

80kg of meat can hold a lot of heat. It cools quicker than you think it would. Also, Japanese families often share the bathwater within themselves(but everyone showers outside the tub first), and the water will become lukewarm at some point in that use case.

> My immediate reaction to this is, “there’s a way for my house to be remotely flooded”.

Yep, remotely operating a machinery will always have some risks. Every machinery should have someone with an emergency stop button should be monitoring it at all time, ideally. But it's a well engineered tub auto-fill in the shower room, it effectively belongs to "inherently safe" category of equipment.