TMK, CI and DL don't cooperate on any sort of "feed" in the US or Asia. If you try to buy xxx-yyy-tpe on BR or CI, you usually get offered flights on anything but UA or DL for the xxx-yyy segment. And, if you're going from the US to somewhere in Asia other than Taiwan, UA and DL steer you towards their JVs.

ETA: I forgot to mention that it's not impossible (not easy, either) to cobble together DL and CI or UA and BR on the same itins when redeeming miles.