If DNS gets a government backdoor, then encryption itself has a master key that criminals, foreign spies, and rogue employees will eventually get their hands on. That's like saying we'll install a secret latch on your front door for the fire department, but somehow no burglar will ever discover it.
DNS is the internet's phonebook. If the government can decrypt and rewrite those lookups, they can redirect you to fake banking sites or impersonate your email provider, and all your other encryption becomes pointless. And if a backdoor is justified here, why not everywhere? At that point, encryption is just theater.