Wasn't this the Bezos directive early on that created AWS? Anything that was created had to be a service with an API. Not allowed to recreate the wheel. So AWS depends on AWS.
My favourite is when some company migrates their physical servers to virtual machines, including the AD domain controllers. Then the next step is to use AD LDAP authentication for the VM management software.
When there's a temporary outage and the VMs don't start up as expected, the admins can't log on and troubleshoot the platform because the logon system was running on it... but isn't now.
The loop is closed.
You see this all the time, especially with system-management software. They become dependent on the systems they're managing, and vice-versa.
If you care about availability at all, make sure to have physical servers providing basic services like DNS, NTP, LDAP, RADIUS, etc...
