They are passively searching the all blue. It clearly is not in the 4 seas because they are easily navigable, so if it exists, it must be on the grand line.
Specially the second part is the hardest to navigate as stated multiple times, so the best candidate for being the hidden place of the all blue.
Is this clear enough?
What do you mean passively searching?
They specifically went from island to island in the Paradise, all following the Log Pose. The route they take is whatever route other people take too, only Skypiea is different. So that's not passively searching, they just ignore it.
Especially in New World, where they have clear objectives from A to B, that's even more farther than "passively searching".
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How do you guys get WCI Wano and a cover story and still think Sanji is more mistreated than Usopp and Chopper?
Because finding new place and new people means chopper gets to learn more about illness, especially in Zou he gets to see their techniques and in Wano he gets to see the legendary medicine.
Usopp fought more and more people, it's his way proving himself as brave man of the sea by overcoming difficulties.
They both progress their dreams. On the other hand All Blue is never mentioned at all by MCs or side characters, and they only travel to known islands to islands.