Earlier quoted context omitted.
They're widely used because they were one of the few providers of geo-aware DNS service for a long time. (These days there are other, cheaper options, including Amazon Route53.)
It's pretty wild that AWS is having impacts for the dyn outage given the shoutout to Route53. Wonder what they know that they don't?
$ dig +short ns amazon.com
ns1.p31.dynect.net. pdns1.ultradns.net. ns4.p31.dynect.net. pdns6.ultradns.co.uk. ns3.p31.dynect.net. ns2.p31.dynect.net.