It's up to the partners to be willing to sell seats at a deep discount (think mid-single-digit hundreds of dollars (plus taxes and surcharges) for NYC-TYO J). If they think the last J seat they sell will be more than that, the partner will not open availability.

With the current limitations on capacity transpacific (mostly due to the steep decrease relative to 5 years ago in US-China capacity, which results in passengers shifting over to NRT/HND/ICN/TPE/HKG connections, decreasing the chances of the likes of JL/KE/CI/DL (to limit to FB partners) deciding to open up availability.

For all-AFKL itineraries, AFKL's willingness to sell (at potentially exorbitant prices) as long as there's a seat available (it's not clear if they'll allow a miles booking which would create an oversale) means that they will normally show an NYC-CDG/AMS-XXX option, but they're not suppressing NYC-XXX. You can see examples of this if you search for SFO-SGN departing on Wednesday: there will usually be the VN nonstop for a hundred thousand miles and AF connecting in CDG for 5x that offered.