At least some machines/routers do NOT have a primary and backup but instead randomly round-robin between them.

Which means that you’d be on cloudflare half the time and on google half the time which may not be what you wanted.

It would depend on how Cloudflare set up their systems. From this and other outages, I think it's pretty clear that they've set up their systems as a single failure domain. But it would be possible for them to have setup for 1.1.1.1 and 1.0.0.1 to have separate failure domains --- separate infrastructure, at least some sites running one but not the other.