Yep - upgrades (other than those paid in cash or Avios) are only "operational" (i.e. where BA need to move people forward to free up an overbooked lower cabin). The sweet spot is to book WTP - from which late notice Avios upgrades to Club (for relatively few Avios) are common, and also not uncommon for WTP to be overbooked. If there is overbooking, then BA GGL/Gold/Silver status should put you higher up the (invisible and unpublished) list for an operational upgrade, although even that is not an exact science.

For context, in 10+ years as a BA Gold (and 5 years as BA Silver before that), I have had 2 "free" upgrades, ever - one from LHR to the US, upgraded from WT to WTP (along with my two travel companions) - I suspect this was a simple overbooking scenario in WTP, and I was a fairly new Gold card at that time. The other, an upgrade from short-haul economy to short-haul business, the first flight after BA lost my suitcase (which I never saw again) - which could have been some form of "apology" but could also just have been overbooking as I had only switched onto that particular flight at very short notice.

In summary, don't expect any upgrades from BA, ever, regardless of status. They'd rather fly Club or First half empty than "give away" their product.