Wait, then why does 1.0.0.1 exist? I'll grant I've never seen it advertised/documented as a backup, but I just assumed it must be because why else would you have two? (Given that 1.1.1.1 already isn't actually a single point, so I wouldn't think you need a second IP for load balancing reasons.)
I don't know of it's the reason, but inet_aton[0] and other parsing libraries that match its behaviour will parse 1.1 as 1.0.0.1. I use `ping 1.1` as a quick connectivity test.
1.0.0.0/24 is a different network than 1.1.1.0/24 too, so can be hosted elsewhere. Indeed right now 1.1.1.1 from my laptop goes via 141.101.71.63 and 1.0.0.1 via 141.101.71.121, which are both hosts on the same LINX/LON1 peer but presumably from different routers, so there is some resilience there.
Given DNS is about the easiest thing to avoid a single point of failure on I'm not sure why you would put all your eggs in a single company, but that seems to be the modern internet - centralisation over resilience because resilience is somehow deemed to be hard.
Not a network expert but anycast will give you different routes depending on where you are. But having 2 IPs will give you different routes to them from the same location.
In this case since the error was BGP related, and they clearly use the same system to announce both IPs, both were affected.
In this case they both are advertised from the same peer above, I suspect they usually are - they certainly come from the same AS, but they don't need to. You could have two peers with cloudflare with different weights for each /24
