Until a few years ago, as a QFF you would only get lounge access with a QP membership. So even when you were on that $1200 one way domestic business ticket they wouldn't have given you access to the QP.
They then made a 180 degree turn by not only allowing J pax into lounges but by creating lounges especially for domestic J pax and OW elites.

So until 3-4 years back the model here looked more like AA than BA. And still today it is the complimentary QP membership which gives a SG access.

I actually don't think there is a big risk of SGs losing QP access. The change is just there to inform people about how much of their purchased membership is left.