I am inclined to say that SQ adopted a "wait and see" attitude when it suspended Pakistan after 9/11. The route was not making major losses, but it wasn't turning in huge profits like SQ's Indian routes either.
As to why they upgraded the aircraft to the 777ER, my guess is that the route did not justify having a 3 class config aircraft (A340).
I do admit that cargo out of Pakistan was good initially, but after CX came into the market, SQ was hit, since cgo agents could now send their cargo directly to North Asia via HKG instead of through SIN. On many occasions, cargo ex-Pakistan were stranded in SIN because priority was given to higher yield cargo from Europe, US and Australia. Cargo ex-KHI/LHE were not high yield and comprised mainly textiles, pharmaceuticals, live crabs and the seasonal mangoes bound for N.Asia. Often, KHISQ was unable to secure space ex-SIN for their cargo. CX was able to offer cargo agents a cheaper and direct alternative.
Now for CX. CX only operated into KHI because they had the aircrafts to spare. So instead of letting their aircrafts sit idle in HKG, and incurring high overnight charges, they chose to utilise them on the KHI route. CX experienced high loads out of KHI in the initial months, but the flights were NEVER full. The bulk of passengers ex-KHI were BKK bound, and only a handful went on to HKG. Fortunately, they had traffic rights on both the KHI-BKK and BKK-HKG sectors, and were able to fill the aircraft to the brim on the BKK-HKG sector.
TG was badly hit as CX marketed itself as a premiere carrier with better inflight products as well as the numerous connections to the US and Canada (lots of Pakistani passengers travel to the US and Canada). Many Pakistanis switched to CX as a result. SQ's US and Vancouver bound passengers also switched to CX since SQ only offered 3 flights a week to Canada from SIN. US bound passengers were often unable to get on the morning flights on SQ because the high yield Indian pax were again given priority. Without the morning connection, Pakistani pax had no choice but to go on the evening flights (SQ30 and SQ2). When this happened, KHI was inclined to provide them with hotel accommodation for the day and that ate into SQ's profit margin.
Right from the start, CX made it clear (at least internally) that KHI was not a high yield market and they weren't expecting turn in profits. It was "good to have, but not critical to the company". To them, the HKG-BKK-KHIvv flight meant an additional flight on the very lucrative HKG-BKKvv sector. Why they continue to operate into KHI, well that's anybody's guess. I guess now that SQ has thrown in the towel, there's more reason for CX to stay.
LX's target market is different from CX or SQ altogether. AFAIK, LX operates KHI-DXB, that itself is a huge market. It would not be fair to make such a comparison.
TG and CX might experiencec 80% loadfactor on this route, but that doesn't mean they are making a profit. It really depends on how much passengers are paying for their tickets. If I may say this, Pakistan is not a high yield market for many Asian carriers.
There's always a better way to fly...