GRRM is attacking the idea of a Messiah not with Dany but instead with Rhaegar. I bring up Rhaegar for it is a nice sidestep that answers the same question without relying on the TV show Game of Thrones which Martin has influence but not control with.
Of course GRMM is doing it with "both characters."
Plus there are dozens of other characters he is attacking the idea with (not just Rhaegar and Dany), it literally goes back to A Clash of Kings (2nd book) as soon as that Red Comet shows up. In fact it was occuring in the first book (Game of Thrones) with the prophecy of "The Stallion who Will Mount the World."
In text Martin has a quote that Prophecy (and thus Messiah / Anointed Ones) is like trying to wield a sword without a hilt, to metaphorically hold fire in ones hand, it is a tool but it also burns you and can create a mess.
(here is the literal quote)
—Dalla to Jon Snow
A Storm of Swords, Chapter 73, Jon Chapter 10 of ASoS.
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Yet the idea GRRM is attacking is actually examined even more so in the non main narrative texts such as the lore books and the spin off books. Showing the country was always unmanageable in a fashion, with dragons and without dragons. Feudalism itself produces this chaos and is inherently unstable from an internal standpoint of feudalism. It is not "healthy" for the goals Feudalism is supposed to embody.
Simultaneously when Feudalism is temporarily stable it is often not conductive to human flourishing. For when it is stable it has often unchecked leaders and such a situation often makes the leaders themselves tyrannical and thus the vast small folk are subject to these corrupt leaders.
Messiahs and Feudalism are just different ways to die, fire and ice. You can still live a good life in Westeros but when you live a bad life it is often not subject to your own individual agency for the system is that corrupt, unstable, and does not lead to good outcomes.
