The sauna situation is simple nudity. It is a social gathering

Giving a bath to a child involves very close proximity and parent taking care of the child's body. So it is a very different type of event.

Consider the difference between father and son being at pool and both taking showers naked. No problem there at any age. And each takes care of his own body.

But in a bath, the parent touches the kid's body. And there comes a time when the kid's sexuality starts to awaken, at which point, you want the bathing to become as "hospital/asexual" as possible so you don't want to be naked in bath with child anymore.

Consider a father/son relationship. About the time the son starts to bathe himself, it is probably a good idea for the father to show him how the foreskin retracts on a adult penis (especially if son can't yet retrtact his skin). Or explain why the dad is circumcised and son isn't. (sonce the son would have noticed the difference).
br> But such talks probably signal the time where it is no longer appropriate for parents to be naked while giving son/daughter a bath and start to give the child more and more privacy/autonomy in bath.