Ummm...  It actually is a bit worse than that. Each segment has the embryonic capacity to produce a pair of legs of sorts. Even the mouthparts and antennae of insects grow from rudiments that develop slightly differently to produce "non-legs".

Still, I take your point.

The short answer is that no, there is no four-legged arthropod, even though some of them have no obvious legs, in at least some stages of some species.

However, there are some teasingly close cases. For example, some butterflies have such reduced forepaws that for practical purposes you could call them four-legged. Then again, if yo would be willing to call humans and Kiwis two-legged, you could call mantids and mantispids four-legged, their front legs having been modified into "arms" for grabbing prey.

But the "bauplan", or bodily developmental architecture, does not deviate from the six-legged plan of insects. They have the least number of legs I can think of among arthropods, though I cannot promise that no parasitic mites have fewer. Juvenile stages of ticks have six legs, but as they mature, they grow an extra pair.

My personal theory is that for higher animals the loss of a limb is often a life-threatening injury (not too sure how true this is. Would it lead to most animals bleeding to death?), irrespective of its impact on mobility, whereas for arthropods, losing a leg doesn't mean the animal will die as a direct result of its injuries.

So for higher animals, there is no point carrying "spare" legs around as the animal would die anyway. But for an arthropod, having a few spare legs would mean the, still living, animal could move around effectively.