I think it is difficult for US carriers to be competitive with CI and BR for flights to TPE. Obviously their labor cost is much lower and most Taiwanese/Chinese travellers prefer their service over AA (language, food, movie selection, FA attitude, ticketing flexibility).

At that time (and still mostly true), neither CI nor BR's C product was nearly as good as AA - no IFE and much less space. I think a lot of high tech companies no longer allow employees to fly J class. That makes BR's Deluxe class very popular. You also get CO EQM on SFO-TPE.

Ever since BR started Transpac service in 1992 and CI got better, DL withdrew service from TPE, NW discontinued LAX-TPE nonstop, UA discontinued SFO-TPE (Corrected, thanks Eva Air) nonstop. This summer, between CI and BR, they offer 4-6 nonstop TPE/LAX (plus SQ and MH) and 2-4 nonstop TPE/SFO per day. That is a lot of capacity.

Then there is the schedule. US carriers have flights that leave the US during the day and get there at night. This does not work with connections out of TPE. Taiwanese carriers tend to have the reverse on the flights coming back which does not work with domestic connections.

The interesting thing will be what happens when/if direct flights between Taiwan and China starts. If the Taiwan carriers are allowed to carry US-TW-Mainland passengers via TPE CKS, the picture might change.

For example, if CI/BR can do SFO-TPE-PVG (some extra flying), it could pull passengers away from US/Japanese/Korean/Chinese carriers. It can also pull passengers from CX for southern China destinations. CI/BR can also hub people out of TPE to China with AA feeding from SJC.