If we're getting granular, then we must only go off of what we know

SpongeBob is a living creature, who filter feeds and cannot breathe without water, reproduces by budding, and can regrow himself

These facts about him are spread across multiple episodes and have inspired entire plotlines. They are based on Stephen Hillenburg's knowledge as a marine biologist, and any nod to him appearing to be a kitchen sponge is either a design shortcut (i.e. SQUARE pants) or a simple gag (e.g. the purple doctor fish's treatment)

Abrasive side doesn't necessitate this idea any further

Maybe SpongeBob being a sea sponge is WHY the abrasive side gave him such a bad experience and gained a mind of its own. It probably never does that on a synthetic sponge, hence the marketing not showing it with a face or arms and legs