The fact that the oldest known living species that hasn't changed in millions of years and still exist is some type of crab.

Actually, it's not, not even close. You're thinking of the horseshoe crab (family Limulidae, the lumulids), which are chelicerates – vastly more closely related to arachnids like spiders and scorpions.

To put this into perspective phylogenetically, if you look at true crabs and the Anomura, you have to "zoom out" on the tree of life to include shrimp, then to include woodlice, then to include barnacles, then to include bees, then to include centipedes, then to include trilobites, etc. until you hit a common ancestor with the chelicerates.

If you're talking about morphology, they're also extremely different, only superficially resembling crabs. For example, limulids outright fail one of the main criteria for carcinization, namely in the morphology of its opisthoma (abdomen; for context if you're curious to look up the criteria, this'll be the "pleon" in crabs). If you look at the ventral sides of limulids and crabs, you'll see they're very different.

This is why it never shows up in any serious discussion of carcinization; it's straight-up not even close to what's being discussed. "Crab body plan" has a fairly specific meaning, not just "eh, fuck it, marine arthropod with a shell and about 10 legs looks close enough".

Moreover, from an evolutionary perspective, the fact that limulids are successful long-term doesn't mean anything about the evolutionary trajectory of anything else. If anything, even if that argument made sense, then it'd surely be "return to limulid".

Side note: if you wanted to argue that extremely old, long-successful body plans correlate with modern evolutionary trajectories, then outshining horseshoe crabs by a few dozen million years are velvet worms (phylum Onychophora), which have been found in the early Cambrian. You can see how similar they look.

(Good further reading for this is Horseshoe Crabs and Velvet Worms: The Story of the Animals and Plants that Time has Left Behind (2012) by Richard Fortey. It's a solid read.)