The problem is that we don't know ... https://en.wikipedia.org/wiki/Insect_flight#Evolution_and_ad...
Evolution strongly favors initial conditions, and doesn't tend to come up with major changes in bodyplans once something is established.
This isn't only true in the pedantic sense in relation to your question, i.e. if you did have something evolving from insects that say added an extra pair of legs it would be a new class of arthropods, so it wouldn't be an insect anymore, but nothing major like that has branched off either insects or spiders.
Insects evolving 4 sets of legs would be a much smaller change than spiders evolving wings, since insects already have all the genetic material to grow legs, but spiders have none of the genetic material to grow wings and would have to independently evolve them.
As an aside you're misusing the term "begs the question", it doesn't mean "prompts a question", it's a reference to a specific logical fallacy that doesn't apply here.
I just made the following calculations: fruit flies for example live 50 days, this accounts for more than 500 generations during a typical human lifespan. They lay up to 500 eggs. Of course survival rate must be very low but just for the fun of it let assume everyone survives (maybe a natural disaster has eliminated predators). This means that during the time evolution has tried 10 new human designs it can try also on the order of 10^1300 new fly designs (500^500).
(To a rough approximation.)
(Yes, it's mixed Latin-Greek, but so are metadata, hypervisor and hexadecimal.)