Maybe the timing can be explained, I think it just draws the criticism because it's the lowest hanging fruit. Like, they weren't necessarily moving farther from the Wall, they might have been quartering the ground, which would make a lot more sense. Why NOT send the guy who was able to find his way across open water to find his home city again, to cut through the switchbacks and loops in their trail and head to Eastwatch in a straight line.

On the other hand, we have things like them just happening to stumble across a group of wights that included one member who was not bonded to their White Walker boss. Jon surviving his immersion in the frozen pond, all while beating the wights who were grabbing him and don't need to breathe (he has untapped fire powers like Beric, would be my explanation, but the show doesn't even acknowledge the mystery of his survival to set up some sort of revelation). The boss Walker deciding to shoot down one of the other dragons, rather than the relevant one, that was helpless on the ground, with all the people getting aboard. The inclusion of red shirts in the party they did not bother to name, just to BE red shirts. The hoops they jumped through to keep Jon from riding Drogon, because they misread something from the books that says you can only ever ride one dragon (even though in "Fire and Blood" there are Targaryens who ride dragons as passengers before getting their own). And then there is the question of where they got the giant chain to haul the dead dragon out of the water to resurrect.