It did but it didn’t…
HWR goal is to stop any other variants of him from existing
His belief is the temporal loom and the sacred timeline is what stops it. He also believes that maybe Loki can handle it for him BUT if a multiversal war happens, which it has happened, HWR will just win it again and become HWR at the end of time with the sacred timeline again. Loki and his third option, no sacred timeline/no loom and free will exists COULD be the thing that ultimately stops/ends Kangs for good if they win the war
Right however right now there is nothing to suggest that his plan with its 2 opinions isn't going exactly the way he wants it.
I mean it's the Avengers. We know that they will ultimately win. However, we can look to someone like Thanos as an example.
Thanos won and as he stated "They couldn't live with their failure." Yes they went back and fixed it, but he still won. His goal was still accomplished, and even with their revision, millions were still lost.
So just because it appears that Loki is "choosing a third opinion" doesn't mean they're on the verge of winning or that this isn't a move that favors Kangs. A war with millions of evil geniuses isn't exact in their favor. Thanos beat them, and he was bound by time. Kangs is outside of time and uses the Infinity Stones as paper weights...they're in for a hell of a time. Too soon to call it.