Is it bad to dry fire a compound bow?

The bench will answer this plainly, because plainness is what the matter requires. Yes. Dry-firing a compound bow is genuinely dangerous, and you must not do it.

When you draw a compound bow, you store a considerable amount of energy in the limbs - on a mid-weight hunting rig, perhaps 60 to 80 foot-pounds or more depending on draw weight and draw length. At full draw, the arrow is the intended recipient of that energy. Without an arrow, the limbs snap forward and the energy has nowhere to go. It does not vanish. It travels back into the riser, the cams, the limb pockets, and the string. Limbs can crack or shatter. Cams can fracture or fly free. The string and cables can snap. Any of these events can put fast-moving hardware into your face, your bow hand, or a bystander. Compound bow limbs under failure do not produce polite debris.

If you have dry-fired a compound bow, even once, even accidentally: do not shoot it again before a qualified bow technician inspects it for limb cracks, cam integrity, and string/cable condition. Carbon and fiberglass limb damage is not always visible to the eye. The bow may look fine and be structurally compromised.

The Committee, in its zeal to simplify the catalogs, did at least let this warning survive - though the bench notes they buried it in a footnote smaller than the warranty disclaimer. The Codex keeps it at the front of the chapter, as it has always belonged.