there's a lot that can go wrong with a hypervisor, even including hiding hardware issues from the guest OS.

We don't think about it because we've been quite spoiled with excellent virtual machine platforms (KVM, Xen and even VMWare).

Those that have worked a lot with VirtualBox will be aware of this, it can be deeply unnerving that VM technology is the default way to deploy things after you've spent sufficient time with VirtualBox. (which: is very good for its original purpose, but not for reliability).

The question is: Does Azure use something more like VirtualBox, or more like KVM?

HyperV exhibits properties closer to VirtualBox.