A hypervisor developer claimed that, even though they only support paravirtualized guests, the virtualization would still be faster on a platform with hardware virtualization extensions.
Does this make sense? And through which mechanism could there even be a performance gain?
Yes. In a very abstract sense, there are two things a VMM needs to do: allow the guest to do things it needs to, and prevent it from doing things it shouldn't. Paravirtualization solves the first part. Hardware virtualization extensions are very effective at solving the second part.