The power Hydaelyn passes out seems to be completely passive and purely defensive, and ONLY defensive against unnatural elements like Primals and Ascians. Our strength is our own, and Hydaelyn's power only comes into play when entities try to "cheat" by way of Tempering and such. She doesn't always give it to folks who follow her agenda, either. We have two cases to the contrary to consider: Saint Ajora, who summoned Seraph Ultima to the world, and Ysayle, who assisted Nidhogg's horde by summoning a Primal, of all things. Hydaelyn is clearly not all-knowing; she bestows her powers on promising individuals, but there's no guarantee that those individuals will do what she hopes they will do.
She struck the jackpot with the Warrior of Light, of course - but even the WoL frequently runs off to do things that have little or nothing to do with her agenda. Thordan may have consorted with Ascians, but that's not the reason the WoL got involved in the Dragonsong War. The WoL got involved because people were suffering, and the WoL wanted to help out. The Dragonsong War was (to our current knowledge) not influenced by the Ascians, and Thordan's plotting and eventual Primal summoning had no effect on the war at all. It took place after we'd ALREADY WON. Nidhogg was dead, his horde was in disarray, and while Nidhogg eventually resurrected himself through Estinien, Hydaelyn did not ask us to do any of that.
The only way Hydaelyn could be said to be guiding the fate of humankind is that she allows a few champions to keep living when they would normally be tempered or dead, when facing off against opponents empowered by Zodiark, individuals who wish to kill pretty much everyone to advance their goals. Once Zodiark and his allies cease to be a threat, we currently have no evidence that Hydaelyn will continue to interfere, and SOME evidence that she will NOT (e.g., Answers lyrics).
It's also worth noting that the WoL's opposition to the Garleans is not influenced by Hydaelyn. The WoL would be fighting them regardless of whether they were an Ascian puppet empire. In fact, MOST of the the conflict with the Garleans took place well before the WoL had any idea the Garleans were an Ascian puppet empire (and, for that matter, well before the GARLEANS even knew the Garleans were a puppet empire, and most of them STILL don't know). The question is, did HYDAELYN know the Garleans were an Ascian puppet empire? That's unclear; it's likely she knew the Ascians were up to something, but she might not have suspected the Garleans specifically. There's plenty of evidence that Hydaelyn is not all-knowing.
A good question to ask is this: If the WoL had never been granted the Echo/Blessing by Hydaelyn, what would they have done? Very likely, many of the same things. They'd still be a paragon of warriors, fighting the Garlean Empire on behalf of the Eorzean Alliance. The Alliance would likely steer them WELL away from any Primals - it would be disaster if such a warrior was Tempered - and the Primals would be handled by the usual ungodly costly human wave tactics. The Ascians likely wouldn't take any particular interest in the WoL; while a powerful warrior, conflict with Garlemald is a good thing in their eyes, and powerful warriors on both sides is both normal and expected.