Although it may be scarce, award availability does exist even on Cathay's most popular routes. I got an award seat for my dad in business class on CX252 next month from LHR-HKG and also managed to find return availability in PE via Paris.

I guess CX's algorithms automatically release a small number of award seats on at least some flights? If that's true, then there will hopefully be more awards being released soon--as CX will presumably be expanding their number of flights in response to the easing of quarantine restrictions in Hong Kong.