I firmly agree that sharing passwords is bad, however I can't imagine a threat model where password sharing among multiple parties is more risky than giving multiple people sudo. As zests points out, practically there is no difference because anyone with sudo can change the root password, they are already root, so the auditing use cases is moot if the logging system can't distinguish between two users sudo sued into root at the same time.
Having multiple admins that need to be able to administrate a system might seem like another case where sudo simplifies things, but isn't that what the wheel group is for? Yes there is an M:N issue between administrators and root passwords and we all know that reusing root passwords across boxes is just asking to get pwnd, but if admins can already ssh into a user that has wheel on a system then that implies that there is another existing authentication system that surely could be used to provide the password in a centralized manner. There is complexity in such a service, but that is only required for the M:N case and if it has issues then it can be fixed once. Busted sudo? You have to push emergency updates to (checks notes) ... literally every EC2 image on amazon. If admin:server is 1:N then password manager, copy, paste, and cut sudo out of the loop entirely.