Not a direct comparison, but as an additional data point, my recent BAH flight in CE is showing as I class, which IIRC correctly is the lowest available for CE. So that seems consistent with BAH booking people into the lowest fare class.
However my next to be taken BAH is from MAN to the USA via LHR. The long haul sectors are in A and I, but the short hauls are in J. Holiday booked many months ago, so there should have easily been availability in lower buckets. So not consistent with my previous statement. Go figure!