1. HA does nothing for the situations of corrupt OS installations, failed services, or any series of Windows related difficulties that can bring a server offline
2. When a host fails, all your guests on that host are going to restart due to HA. This means most of them will boot before the Domain Controller, and thus, fail to boot correctly. You'll also find that, during this time, all the guests on unaffected hosts are also offline, as they have no DC.
In short, a DC is something very easy to make a second of, you'd be hard pressed to come up with an argument not to do it. A server with no other roles can run on 1GB RAM and use virtually no CPU.
Edit: The terms "Primary DC" and "Backup DC" make no sense, as Domain Controllers are Multi-Master. Neither will ever be a "backup".