I think the reason people complain about the aircraft on BKK more than any other is that it's easy to benchmark it to what you could have flown had you chosen another carrier on this route - EVA/Thai direct or basically any European or Middle Eastern carrier if you are willing to just slightly lengthen your journey. On many of the other routes where BA operates these 777s there is little-to-no real competition. Having said that, I completely understand BA's strategy here as the problem with BKK is that BA's lunch has basically already been eaten. BKK presents a fairly unique set of issues for BA as a route - leisure-heavy, more budget-led than premium-led and eastbound too.
BA is a premium-heavy airline with largely premium-heavy configured air frames as a result, so they are limited in the frames they could use profitably on a route like BKK, most have just too many J/F seats in ratio to Y for a route like BKK which is largely Y demand. Even worse, a lot of the premium demand that does exist is leisure travel rather than the business travelers that BA usually rely on. This means the average BKK customer is much more willing to fly via the Middle East for what is perceived as a more comfortable product, so BA isn't able to rely on being the quickest and only direct option to drive high premium cabin pricing as they are able to do on many other routes. The fact DXB and DOH don't add much flying time to the route just makes things worse in both Y and J, I have no doubt if EK/QR/EY didn't exist BA would probably be operating multiple BKK rotations a day instead. Finally, on westbound routes BA has an inherent advantage as flying anyone but BA on many of the routes BA offers from LHR involves backtracking and adding significant additional flight time, in addition to also being a viable option for people connecting from other European airports where LHR isn't a significant westbound detour. For BKK the additional time added by changing flights in CDG or FRA is much less than for westbound flight and LHR isn't well placed to attract customers from Continental Europe without offering rock bottom prices (hence the AMS-BKK J fare that has existed forever). In short, I think it's probably more likely BA will drop this route or switch to a smaller aircraft (788 would probably work) than upgrade the product they offer.