Not sure what you're saying.Well, to me it seems a bigger disconnect to say "in this scene you go first because of your high perception score/result" but then also say "but you havent seen a thing that gives you reason to go do anything".
I like having initiative be perception based but it would seem to me that that should be a perception check in full - used for spotting too, not just a half-check. That would resolve the conflict and help the sequence in the scene make sense organically.
This has the feel of a "look down the alley for ogre I was chasing" where you see the ogre but miss the dragon cuz you were looking for ogres.
Let percrption checks be perception checks and let the GM use those for initiative order - fine. But making initiative checks be percrption checks that dont determine perception is... conflicted.
In 5e play, a GM can let initiative be percrption based, because its an ability check by using the variant scores ruke, but it's not required to be separate. When visibility was compromised, I have done it more than a few times.
On one hand, your post could be construed to accuse me of being that "nope, no ogres here" GM...
On the other, you seem to actually engage with the issues at hand when you identify the disconnect and say you're conflicted.
So I guess I'll better defer any comment.