Not my experience. I've had at least 4 occasions since being Gold where my SFO-LHR has been J7, J8 or J9, W0, Y0 or <3 the day before/day of the flight, and I've stayed in the WT+ seat I booked, often booked in W class.

I suspect the chances vary considerably by route.

I'm flying that route next week and the availability for my return is currently at F2J9W0Y7. I'm in WT+.

I fully expect to reply with my "told you so" message from 30D (booked too late to get the bulkhead seat)