PowerDNS Recursor docs[1] mention thousands of requests per second, so maybe they could do 15M = 15K × 1K servers?
Between possible implementation improvements, clustering overhead, regional endpoints, and overprovisioning for peak load it gets fuzzy quick.
> A quad Xeon 3GHz has been measured functioning very well at 400000 real life replayed packets per second.
So that's more like 40 servers. Realistically the complexity of serving DNS is probably somewhere between Fortunes and Json Serialization in the Techempower benchmarks: https://www.techempower.com/benchmarks/#section=data-r21&tes...
So it's possible you could do it with 10, far less than you'd want for proper redundancy.
Packet count obviously matters, but a KV cache lookup followed by a short reply in the usual case is one of the easiest loads to engineer for
Edit: eastdakota's tweet says 13% of the requests are https- or tls-encrypted. That throws a spanner into these calculations.
Cloudflare probably runs 1.1.1.1 on all its servers in 300+ locations worldwide.
DNS isn't hard to serve at that scale compute or bandwidth wise, your problems are more administrative and maintaining enough overhead for misbehaving clients to accidently DoS you.