Why do plastic case laptops warp in short order? I have never seen or heard about that.

It is not so much 'plastic' but 'flexible plastic' and the lack of a stiffening internal frame which causes problems.

I've seen a few 'consumer' laptops - HP DV6000, several Acers - go bad this way with parts on the board loosening. What these models had in common was that none of them had a stiff inside frame but consisted of a plastic bottom on which the guts were screwed down and onto the back of which the screen hinges were mounted with 2-3 screws each. This was capped with a plastic top into which the keyboard was mounted. With all parts removed the top and bottom shell are quite flimsy so any stiffness in the finished product depends on all parts being screwed down tightly. Now add those screwed-down hinges on the back which make the thing flex every time the screen is opened and closed, lift the thing using one hand every now and then which causes it to flex as well and you have a recipe for loosening parts - especially BGA components - on the mainboard.