"AFAIU the root DNS servers will refuse requests for recursive resolutions."

All the DNS data served by the "DNS root servers" is public and available for download via HTTP or FTP request.[FN1] As such, IMHO, there is rarely a reason to query those servers for the data they serve. I already have it.[FN1] For example, the IP address for the "a" com nameserver probably will not change in my lifetime. I am so sure of this that I have it memorised as 192.5.6.30.

A simple illustration of how to reduce DNS queries to one and reduce remote DNS queries to zero. Compile nsd as a root server using --enable-root-server. Add DNS data to a root.zone. Bind nsd to a localhost address, e.g., 127.8.8.8 and serve the zone. Configure the system resolver to query nameserver 127.8.8.8.

      mkdir /tmp/nsd-01
      cd /tmp/nsd-01
      echo . 86400 IN SOA a.root-servers.net. nstld.verisign-grs.com. 2021101501 1800 900 604800 86400 > root.zone
      echo example.com 1 IN A 93.184.216.34 >> root.zone
      test ! -d /nonexistent||rm -rf /nonexistent
      groupadd nsd-01
      useradd nsd-01 -g nsd-01 -s /bin/false -b /nonexistent -d /nonexistent 
      chown nsd-01 /tmp/nsd-01 
      chgrp nsd-01 /tmp/nsd-01 
      printf 'server:\nipv4-edns-size: 0\nzonesdir: "/tmp/nsd-01"\nzone:\nname: "."\nzonefile: "root.zone"\n' > conf
      nsd -u nsd-01 -4 -a 127.8.8.8 -c conf -l log -P pid -f db
      cp /etc/resolv.conf resolv.conf.bak
      echo nameserver 127.8.8.8 > /etc/resolv.conf
      drill -oRD example.com 
      # cleanup
      mv resolv.conf.bak /etc/resolv.conf
      kill $(cat pid)
      rm -rf /tmp/nsd-01
      sleep 1
      userdel nsd-01
      

FN1. How to get the DNS data that the root servers provide, without using DNS:

   x=$(printf '\r\n');
   sed "s/$/$x/" << eof|openssl s_client -connect 192.0.32.9:43 -ign_eof 
   GET /domain/root.zone HTTP/1.1
   Host: www.internic.net
   User-Agent: www
   Connection: close

   eof

ftp://192.0.32.9/domain/root.zone

FN2. Except in emergencies where I have no access to locally stored root.zone DNS data. Also because I have the "a" root server IP address memorised as 198.41.0.4, I sometimes use it as a ping address.