I have to say I never experienced such a situation in 25 years. What kind of problem would require a root login, while at the same time it doesn’t cause a service downtime anyway? You mentioned LDAP – Well, if all of your LDAP services are down at the same time, and root is your only non-LDAP account (which would be a very bad idea, by the way), then your services are probably down anyway because authentication doesn’t work anymore.
When an organiation gets large enough, the staff moves and changes need to be centrally managed so there is a highly secure single source of truth for accounts, authorisations, and password.
This is typically done with some combination or adaptation of Kerberos and LDAP, which rely on the network for their function.
There are many reasons why the LDAP servers may become inaccessible -- and those reasons go well beyond the risks that can be managed by clustering or running multiple lines of LDAP service.
There have been many occasions where I have seen a Unix host disappear from the network, suddenly and unexpectedly.
When you have hundreds of VMware servers, dozens are going to get replaced every year with the ongoing hardware replacement programme. This provides a common source if problems -- because it's really hard to test properly before new server is commissioned.
When a Unix VM disappears from the network, your only way in to that Unix system is via the virtual console furnished by the VMware server. You have no network, and therefore no LDAP authentication, so you can't login as yourself, and you absolutely need a local root login to diagnose the problem. The most usual cause of this problem is a recent VMotion of your Unix VM to a new VMware server configured without the VLAN(s) your Unix VM needs to operate on its network(s). The second most common cause is that the firewall team got the firewall rules wrong for the list of VMs that may be migrated to the new VMware server. Host-based firewall rules on your Unix VM may also come into play, but that's far less common.
Such problems do not justify shutting down the Unix VM (and losing state and any stalled transactions) because the network is down and you can't login! All you have to do is is fix the network issue(s).
Besides, shutting any system down without a pre-approved scheduled outage would most certainly result in a Quality Assurance non-conformance notice arriving in your in-box.
So, there exist circumstances where root logins are both desirable and necessary.