My biggest concern with encrypting the host is that a password will be required to boot the Hyper-V server, and thus their serves will not boot until that has been done.

TPM is what allows that not to be the case, although I still haven't personally figured out exactly what does and doesn't trigger bitlocker recovery mode; I think hard power off might.

Hyper-V can create virtual TPMs for the guests in order to enable Bitlocker within them; If your host server has a TPM you can enable Bitlocker on the entire system, but I've never done that myself, and I'd be very skeptical of doing so for common sense "can you imagine if that got messed up" reasons.