That seems to not be the reason from the latest data. Insect oxygen transfer basically doesn't scale cleanly with oxygen in the atmosphere like the original hypothesis thought.

What IS true though is that pterosaurs and later birds and bats came onto the scene, and that's just game over for giant dragonflies.

Vertebrates have 2 essential advantages over insects, at big enough sizes.

An efficient circulatory system and myelinated nerves.

At small sizes, the circulatory and respiratory systems of insects work better (less friction for blood in the absence of capillaries and less friction for the air that circulates as a gas through the body), but at big sizes those of vertebrates work better, due to efficient pumping.

The myelinated nerves have the same speed for propagating nervous signals as non-myelinated nerves that are much thicker, so thick that an insect could not have many such nerves. At small sizes this does not matter, but at big sizes if the nerves are not fast enough the reaction times of an animal can become too slow, e.g. the head might need a big fraction of a second until noticing that something bites the tail.

The combined results are that an insect as big as a typical vertebrate would react mostly sluggishly and it would be able of only very short bursts of intense activity, before becoming tired. This would put it at a serious disadvantage.