I’m also surprised that traffic from Cloudflare DNS users caused any significant problem. Was it really that much traffic?
It's not. The proof is that CDNs existed long before edns-client-subnet was introduced. All it does is allow the CDN's DNS servers to return the most optimal A/AAAA records for the client. But the worst that should happen without it is you get sent to a more distant CDN server, and the content loads more slowly.
The fact that archive.is somehow suffers without this feature (which, btw, wasn't standardized until 2016) suggests they're doing something really, really odd. If I were them, I'd focus on making my system more robust, rather than demanding the rest of the Internet adopt a relatively young, optional DNS extension.
Here's an interesting thought — if it's so bad for privacy and isn't necessary for a CDN, does Cloudflare the CDN simply disregard ECS when receiving requests from DNS.Google, or do they take it into account?
It's not because it can be bad for privacy that you can't use it for good. The feature exist for a good reason, it's valid, it doesn't change anything to the fact though that it can be use for bad reasons too, which is why you want to remove it. In the means time, there's no reasons not to use it for good reason while it's still there.