A lesson in the Bible that shows us God's consistency in choosing not to take away the source of particular judgments is in the last book of the Bible. This sheds light on the Numbers 21:6-9 episode due to parallels as well as differences.
The Revelation account shows God pouring out from heaven various plagues upon an increasingly godless, faithless world. Chapter 9 starts to detail three woes sent from heaven to earth. Note these observations in this book:
"Why such things sent from God? Only if so be that men would
acknowledge the truth in heaven and earth, before God and man, and
come to repentance in time, or ever the certainty of an infinitely
worse and eternal judgment should be brought to pass at the sounding
of the last trump.
Such events were initiated in heaven by the Lamb of God, who broke the
seventh seal, and called forth the seven angels, commanding them to be
given seven trumpets... what is the effect upon the inhabiters of the
earth, upon the world, of such a true gospel, accompanied by the
sounding of such trumpets, increasingly warning mankind of the looming
judgment to come?
(Rev. 9:20-21) And the rest of the men [namely, of the remaining two
thirds on the earth] which were not killed by these plagues yet
repented not of the works of their hands, that they should not worship
devils, and idols of gold, and silver, and brass, and stone, and of
wood: which neither can see nor hear, nor walk; Neither repented they
of their murders, nor of their sorceries, nor of their fornication,
nor of their thefts." The Revelation of Jesus Christ, pp 236-8, John
The parallels with Numbers 21 are rebellion against God, judgments against them being sent by God, the need to repent of their sin that brought these plagues, and faith to look up to see the heavenly source plus to put faith in God so as to repent and be spared.
The differences with Numbers 21 are a global situation instead of a national one, and people not in covenant relationship with God also being judged.
Perhaps the most significant point is how both accounts require people to look up in faith to the One this is all about - Jesus Christ, the Lamb of God.
In Numbers 21, nobody is to worship this brazen serpent on a pole; they are to look up to it as God's means of deliverance from the plague. In other words, instead of expecting God to take away the plague, they accept that they deserve the plague (confession) and trust in God's apparently strange way of counteracting the consequences of their sin (by faith). Only after they do that are they healed.
It's the same with the modern counterpart, in our world today where plagues are increasingly afflicting mankind. God consistently judges sin and punishes the people who refuse to acknowledge him - in Revelation, on a global scale. The call is heavenly, as in Revelation 14:6-7:
"And I saw another angel fly in the midst of heaven, having the
everlasting gospel to preach unto them that dwell on the earth, and to
every nation, and kindred, and tongue, and people, saying with a loud
voice, 'Fear God and give glory to him; for the hour of his judgment
is come: and worship him that made heaven, and earth, and the sea, and
the fountains of water."
But are the nations looking up? Do they even think there could be a heavenly messenger calling them to hear the gospel of Christ? If they but looked up instead of being fixated on the ground where they experience plagues whilst seeking earthly pleasures, they could see Christ lifted up, as was that serpent on the pole in Moses' day. John 3:14-15; 12:31-33; 16:7-11.
It was the same John who wrote those verses showing the crucified and risen Lamb of God to be the fulfillment of the brass snake in Moses' day who also wrote the Revelation about the global fulfillment in our day, with an invisible serpent exposed as leading them into idolatrous worship. In both situations, those who would be healed by God don't suppose God should just take away the cause of their sufferings; they learn the lessons of their own sin, their need to turn from idolatry, to repent and put faith in the one lifted up high.
In both cases the requirement is to repentantly look up in faith, believing in God's unique means of deliverance. That's what transforms situations of suffering into healing. That's what deals with death and gives life.
Numbers 21 points to John 3:14-15; 12:31-33; 16:7-11 - and that, in turn, points us to Revelation 9 for those who look to the uplifted Christ are granted to eat of the Tree of Life in the Paradise of God - Revelation 22:2-4.