CDC data are disappearing

That doesn't matter anymore. No one believed the CDC data to begin with. You think they're going to believe it when it comes from third-party backups?

I think the benefit is not just from regular people having access - but other researchers who do need/trust the data.

The problem is that the provenance of that data will be questioned. It’s one thing that researchers will trust and use that data, but that citing these archive sites will fall flat when their conclusions have to exit academia and be subject to extra scrutiny.