The unencrypted backup system is almost certainly implemented mainly to give government authorities easy access to chat history when presented with a warrant whenever possible. Since this is offered as a helpful feature, very few think twice about the part in asterisk. This way they can comply with warrants without backdooring their app while continuing to sticker label "end to end encryption" and giving people comfort that their data is in "their" drive. There's no other reason really for such a weird arrangement.
That doesn't make much sense. There is no such legal requirement (hence the discussion). The Google backup option isn't universally used. And WhatsApp controls the key generation and management and could easily integrate any other sort of more robust backdoor. Such as their previous system, as described somewhere in this subthread, of storing the key on the server to allow recovery.
I'm not saying it's a legal requirement, I'm saying it's likely a smart tacit compromise.
On one hand - even after end to end encryption, we continue to see WhatsApp messages quoted in prosecution including in SEC actions and prosecutors are clearly getting access to messages even pre-arrest. The ability of prosecutors to compell unlocking after arrest in US is questionable. So how are they getting access to the messages if there's truly end to end encryption? Also there are any number of Governments in the important non-US markets that would simply ban WhatsApp if they didn't have access against a warrant (eg. See BlackBerry cases from some years ago)
On the other hand, no security researcher seems to have found or at least reported a back door in the WhatsApp apps that supports MITM undetectable to physical key verification which is the obvious weakness in an end to end encryption system based on centralised key repository system.
On the gripping hand, all high profile cases trying to compell tech companies to provide evidence have been against Apple. I've not heard of one against WhatsApp.
Ergo - the most like scenario is that this feature is deliberately built keeping messages un-encrypted so that when law enforcement shows up with a warrant or a muzzled warrant, they can just hand over the archive without weakening their app. People are convinced to opt in because it's the only way to change devices while keeping your messages. To give people comfort that unencrypted messages ate safe, it is sold as as "it's in your own Google drive"