Since Aaron37 has now admitted (sort of) that it is not a sin against God for believers to discuss or even debate doctrine with one another, I suppose I can continue then. (Although I wish someone else had asked the question instead anyway.)
As might be expected, I already covered this in some detail back in Part 4 of my detailed analysis of the final chapters of RevJohn.
The short answer is that if the kings of the earth and their followers (who are the targets in view here in chp 16) are being shepherded by Christ even in their destruction (which is explicitly said in Rev 19), and are found in the final chapters going into the New Jerusalem where unrepentant sinners cannot go–not unless their names are written into the BoL (which is also explicitly said)–following the light of Christ; then obviously they do in fact eventually repent of their sins and go in. It just takes the lake of fire judgment to lead them to that point, and we aren’t at the lake of fire judgment yet in the revelation by this point.
So the real debate is actually about the final fate of the kings of the earth (also known in this chapter as the kings of the east), not about their lack of repentance here. This is only a revelation that they won’t repent before then: there will still be rebels gathering together under the ten kings of the earth for the war of the great Day of God the Almighty Who is about to be coming upon them like a brigand. (Preparations and foreshadowing for this are at Rev 16:12-16; but it doesn’t finally happen until Christ arrives to shepherd them with the rod of iron at Rev 19:11-21. Several other foreshadowings for it, too, in surrounding verses and chapters, for example Rev 14:14-20.)
Most importantly, though, while John is overlapping what’s going on with foreshadowings of what will be happening later, he also takes a moment at the very start of the sign of the seven plagues of the bowls of wrath (which are the last because in them the wrath of God is finished, Rev 15:1) to foretell what the end result of this is going to be.
The end result of the finishing of the wrath of God (before the finishing of which no one will be able to enter the Temple, 15:8, but by connotation after which they will) is that those conquerors (a term used for those who repent of their sins and overcome them in Christ) who come out from the beast and out from his image and out from the number of his name, will be standing upon the glassy sea mixed with fire, holding the harps of God and singing the song of Moses the slave of God as well as the song of the Lambkin, praising God for His ways of justice and truth; and rejoicing that there will be no one who does not fear Him and glorify His name but that all the nations will come and worship before Him. (Probably a quote from Psalm 86, where David predicts that all the nations made by God will reject their false idols and come to worship Him some day–also rejoicing, among other things, that God has delivered his soul from Sheol.) The Song of Moses, meanwhile, is the prediction that after God totally destroys those who rebel against Him to the uttermost limit (rebel Israel being mainly but not solely in view), then they will acknowledge Him as Lord, and repent of their sins, and He will restore and vindicate them as His people (which they always were, though rebels).
After revealing the ending, God goes on to show John the terrors of the seven final bowls; where certainly the kings of the earth and their dedicated followers are not fearing God and giving Him glory, much less setting aside their idolatry and coming to worship Him. Not yet: Rev 15:2-4 shows they’ll come around eventually, and leave the beast, his image and his number–they’ll even leave the lake of fire, in a way (or rather it becomes the foundation holding them up: as the Holy Spirit should.)
Until then?–they’ll be tread in the winepress. Be we also know the fate of even those who are tread in the winepress: they eventually submit to Christ and are brought to the Father in the submission of the Son, so that God may be all in all (1 Cor 15:20-28.) Because true love never fails, never gives up hope, endures all things and keeps going. (1 Cor 13.)
(By providence, I happened to be listening to a boys choir sing “A Brand New Day” when I was writing about those coming out from the beast and from his number, standing upon the sea of fire and praising God for His salvation. Had to stop a moment to praise God in worship, too. )