I think the bigger question is why do cereals come in boxes at all?

Lays is trialling then in the Netherlands at the moment and people are unhappy with chips going from €12/kilo to €20/kilo

https://www.jumbo.com/producten/lay-s-bugles-nacho-cheese-chips-snackbox-135g-711678STK

Your cereal bags are recyclable? They aren't also in cardboard boxes?

The heat would cause loads of condensation and ruin the lot

I'm not familiar with cereal bags being accepted for recycling at grocery stores -- although I'm aware that grocery store recycling in California has deep issues regarding implementation -- but regarding why a chip bag is different than a cereal bag, my guess is that it has to do with the former being air tight.

Chip bags are intentionally filled with gas (usually nitrogen) in order to preserve the contents for a long shelf life. Rather conveniently, this also helps the chips not smash up against other chip bags in the same box, at the cost of fitting fewer bags into a shipping container. As such, chip bags have to be air tight, and mylar is good at that, as evidenced by mylar balloons that keep helium inside for far longer than a latex balloon (to the sadness of every electricity provider on Earth).

Whereas I suspect the clear plastic -- maybe polyethylene? -- bags used for cereal have different requirements, because a cereal box already provides mechanical protection against other boxes, and an expectation that cereals (a bona fide breakfast foodstuff, compared to chips which have always been categorized as a snack food) will be eaten in quantities that make recyclability a priority; this is a guess.

I also think cereals might historically have been just free-floating inside the box, in the same way that dishwasher power detergent is still packaged within a thick cardstock box, with a pour-out metal spout. That said, this citation seems to indicate that cereal bags are in-fact liners, which would suggest the primary reason is one of food safety, if contact directly with the inside of the box would be a problem.

And this kinda makes sense to me, since nobody would want to eat soggy cereal if a bit of rainwater seeped through the box and contacted the food.