Every definitive trait has some counter example that still counts because people “feel” it’s good enough.

There’s an aphorism in statstics / science: “all models are wrong, but some are useful.” I feel that the distinction between genuine off-road-capable SUVs and crossovers/tall cars/glorified station wagons or minivans is useful, even if it isn’t completely definitive. Generally speaking, if it’s a unibody vehicle it probably isn’t very good off-road, and therefore doesn’t really deserve to be called an “SUV.”

So does a 2wd “suv” (by your definition) then get declassified?

A 2WD SUV is less general-purpose, but I think they still have enough potential to count (think desert-racing prerunners, which are often 2WD but legitimate off-road vehicles).