I think people are looking at the subject too narrowly.
We know the Echo protects against tempering; that's been empirically demonstrated with numerous other sources. That said Hydaelyn tempering the PC is predicated on the argument that "Hydaelyn is more powerful than typical primals, so (maybe) she can overpower the Echo like Zodiark (maybe)."
Can she, though? Even at her apex Hydaelyn wasn't anywhere near as powerful as Zodiark (a small council vs. half of Amaurot's population), and she's only grown weaker as time has gone on (empirically demonstrated with Matoya's Crystal Eye - an ancient Crystal of Light). Is it possible Hydaelyn can overpower the Echo? Sure, it's possible. Given her power is almost completely exhausted even before the start of the game... I'm not so sure she can. I mean, Zenos' grand master plan falls apart if that's the case...
Second, there's no reason to believe the Echo's immunity to tempering means we're incapable of receiving Hydaelyn's blessing; the blessing is not necessarily tempering, in other words. Ifrit's dialogue is phrased in such a way as he considers tempering "blessing," and Hades' EX dialogue supports this idea ("We are the blessed! We are the chosen!"), but there's no reason to believe a primal couldn't bestow power upon a mortal without tempering them. Most primals just wouldn't do such a thing, since there's no benefit in it for them and the vast majority of summoned primals in the modern day use summoning arts designed to play up the worst aspects of the summoned creation, but not only is Hydaelyn from before then she is very unusual in regards to primals in the sense that she freely gives of her power to help mortals.
Third, there's no clear point at which the PC is tempered. They implicitly awaken to the Echo on the carriage ride in, do good deeds in the starting capital, get the Water Crystal and get talked at by her for the first time, and then go on the whirlwind adventure of 2.0 fighting primals and Imperials. Tempering is kind of a big deal; when exactly did that happen? And if the Blessing of Light is "just" tempering, why is Midgardsormr able to seal it away? Could he have cured tempering all along? If so why didn't he help Tiamat (and other tempered victims on Hydaelyn's order)? Were we acting fully under our own will then and not before? Did restoring the blessing restore the tempering? Wouldn't we have noticed? Why do the Ascians specifically refer to it as the "Blessing of Light," and never tempering (or a consequence thereof)?
Last... there are numerous instances of Hydaelyn's blessed chosen defying her will, as has been pointed out before. Ysayle consorts with the Ascians and summons a primal. The Warriors of Darkness consort with the Ascians and attempt to usher in another Calamity. Saint Ajora summoned Ultima, an immensely powerful and dangerous primal. In all those instances compelling those people to not do those things would very much be in Hydaelyn's interests, yet her chosen champions stray from her path and consort with Darkness.
Again, that's not to say Hydaelyn is unwilling or incapable of tempering, but all the evidence of such regarding the PC is circumstantial, and thus the case isn't terribly strong. In my opinion.
Remember, the following is always technically true:
Hydaelyn's account of the origin of her conflict with Zodiark conflicts with Emet-Selch's... but the two aren't necessarily mutually exclusive with some imagination. Even then, we haven't heard her side of the story yet (something Yoshi-P himself has noted; look forward to it in Endwalker, probably), and without that I personally feel saying "She lied to us and must be put to the sword for it" is seriously jumping the gun. The very worst she's been portrayed is as a cosmic level Urianger: deceitful but well-intentioned. Compelling anyone to do anything doesn't fit her character as it's been established.