As an example, consider a user in Paris, and assume for the sake of this example that Cloudflare's closest POP is in Berlin. Assume that user visiting a site hosted by a French CDN, with POPs in both Paris and Berlin.
If that user tries to resolve cdn.mysite.fr via 1.1.1.1, they'd get a Berlin-based location, since the French CDN has no way of knowing that the user is actually closer to them, and Paris would have been the better option.
Anycast isn't magic, and it can't be used in all situations. For example Akamai has 16 times as many POPs as Cloudflare does, and many of them reside within smaller ISPs where you might not be able to establish BGP sessions. Long running downloads and websockets are better served over unicast addresses. Not to mention you don't have a lot of knobs to fix things when anycast does go wrong and you have a network in the US sending your traffic to an EU POP because they have cheaper transit in Europe.
You might find this work from LinkedIn informative: https://engineering.linkedin.com/network-performance/tcp-ove...
Which makes it all the more dubious to block it…
DNS traffic has good traffic ratios, at least compared to typical http traffic. That's got to help with peering negotiations. Although DNS traffic isn't that much, so it probably doesn't help much.
Same for accepting and dropping inbound volumetric DDoS. Larger ISPs want to see roughly balanced inbound and outbound flows before they'll agree to settlement free peering, and options for attracting inbound flows from residential ISP customers are limited (run a backup service, run a 1:1 multimedia messaging service and/or video chat, DNS helps a bit)
Also, by running their own DNS they can ensure that some percentage of the Internet does NOT cache results beyond what they want (to some extent) - much of what Cloudflare does is DNS trickery to route to the appropriate CDN.
And from a corporate perspective, historically no one ever got fired for using IBM. Who would you want running your Fortune 500 corporate CDN, a company that can handle 1.3T reqs/day or another CDN provider that's one-tenth the price but doesn't have the scale/reach of Cloudflare?
Akamai is IBM in this example. They are "enterprise" and have been long before Cloudflare existed and have 4,200 POPs compared to Cloudflare's 250.
Users need working DNS to use Cloudflare’s paid services. That used to be a business in and of itself, where OpenDNS made money showing people ads. But now the market price has been driven to zero.
To quote: The "other than data-mining" part is still unanswered
I'm not saying they will do this, but they could if they wanted to. I've seen this from DNS providers in other countries.