The fact is that on a BA award ticket BA charges whatever carrier imposed surcharges the operating carrier charges on a revenue ticket, whether it be coded YR or YQ. Whether this is labelled a fuel surcharge or carrier surcharge is really irrelevant as the consumer is really just interested in the total cash component.

BA also no longer calls their YQ charge a fuel surcharge but rather a carrier surcharge, but personally I would not claim that BA "does not charge a fuel surcharge on BA redemptions" just as I would not say that BA "does not charge a fuel surcharge on CX redemptions" as you claimed.

Yes, the carrier imposed surcharge is low on a CX redemption but it is still present as highlighted above. CX could increase their YQ to any amount (subject to local regulations, ex-HKG they are restricted for example) and BA would pass this on.