BA CCRs are for their F pax and they have them at JFK (i've never seen it packed) at T5 (again busy but never packed from my experience). I haven't found the CX F lounge in HKG ever overly full, nor the JL F lounge at NRT, so I can't really agree with OP's comments.
The only places i have seen F lounges overly stuff is the tiny AA FL in ORD. I've never noticed JFK or LAX FLs as being too full.
I actually see (as others have said) the OW lounge policy as a big plus over the other two alliances.