I don't think that GRRM is attacking the idea of a Messiah, I think he's trying to build on and improve fantasy concepts. I think he's going for a new and improved version of a messiah, with both or either Dany & Jon. I don't doubt his ideas are not far from what you suggest, but I don't think the book series is all about tearing down Dany and saying she's an example of a bad thing. With two (or possibly more) books to go in the series, Dany has already taken the first steps down the dark path, which is WAAAY too long to be wallowing on it for it to end with her tragic death. I think, rather, her "dragon plants no trees" epiphany at the end of the last book is taking her to a Dark Rand place, not a "oh no, I unleashed an unstoppable tide' Paul Maud'dib place or a 'kill everyone who won't get on board with my vision of a better world' place that the show asserted she was in (without entirely successfully portraying that) when Jon offed her.

I don't think the show can be taken seriously as an indicator of the books' endgame. Maybe some of the events in the last seasons of the show can be hints at events in the books, but for their context and meaning, I think we're on more solid ground looking at the earlier books to extrapolate forward. The show subverted the messiah trope for shits and giggles. They went along with the books' portrayal of the rise of a messianic hero, and where they deviated from that (such as the changes in Qarth - in the book, it's a place of temptation, intended to arrest the hero's momentum & lure her into indolence, as well as providing dreams and visions to entice her in other ways; on the show, it's just there - the books say she stops in this city, so lets do a dragon-napping plot, because its cheaper than the visions and prophecies for a story we haven't mapped out yet), it was not deliberate, but a lack of logistical capacity to portray the story, or a failure to grasp what the story really was. They had Arya actually strike the deciding blow against the existential threat simply because everyone was expecting it to be Jon or Dany or Bran, or just possibly one of the fire-relevant people and the showrunners went for shock value, rather than story coherence.

I think Martin's treatment of a messiah is going to sort of acknowledge that being a messiah is something of a cheat code at politics, as you allude above, but where Herbert was intent on showing how dangerous and bad that is, Martin is going to show what it's really for. Not ruling a kingdom, but saving lives, at a place where divisions of race, religion and ideology are irrelevant. I think Herbert would have agreed with that too, he simply did not insert the sort of messiah-relevant threat that Martin or Robert Jordan did, and instead, came up with a worthy target for his messiah(s), Leto II's Golden Path, to save humanity from whatever he and Paul foresaw (I'm not super clear on that, since the antagonists at the end were basically Leto's creations). Martin's not shooting that high, he's doing things on a more "Wheel of Time" scale. And he's going to get into the personal costs for the messiah characters, he's going to explore what it means for the people in proximity to them, and what saving the world is going to entail. I think Martin WANTS to get to a happy ending, he just rejects "happily ever after" because he knows there are no solutions to real problems, just trade-offs for more manageable ones, and that "happily ever after" takes a lot of work and ongoing maintenance. Martin is on record concerning the ending of "The Lord of the Rings" as liking the scouring of the Shire, and not liking the HEA wrap-up of Aragorn's taking the throne of Gondor. The former entailed more work, reflected the sacrifice of Frodo in saving the world for others, and went into details as how the happy ending was happy and how it came to be. Whereas Aragon, just ruled well for a long time, according to the book, with no details, like who got the short end of the stick, what sort of efforts were made to cleanup Gondor, like the replanting in the Shire, and so on. We find out how the ownership of Bag End was settled, and what arrangements were made to fit the Shire into the political framework of the rest of the setting, but not a lot about that framework. Where there other regions and borders like the Shire in Aragorn's realm? How did Rohan fit in? What I find most interesting is that Aragorn refrained from even setting foot in the Shire, and that when he'd come by to visit his hobbit buds, he waited outside the borders, and they came out to meet him. It's like Tolkien was acknowledging that there was something off about even a hero king, and even a friendly visit from King Elessar would disrupt the happy idyll the Shire was supposed to have become. Dr. Kynes, the father of Liet, would probably agree wholeheartedly, even if he would have been bored silly in the Shire by the time Elanor Gamgee was a toddler.